Skip to main content

Textbooks

Calculus Textbook Answers

Browse Calculus Textbooks with Answers to Popular Problems

$Calculus$

Browse bartleby's library of Calculus textbooks to find answers to your specific homework questions. Have Calculus homework questions? Study smarter with bartleby’s step-by-step Calculus textbook solutions.

Calculus: Early Transcendentals

Calculus: Early Transcendentals

Author:James Stewart

Cengage Learning

A function f is defined as a ordered pair (x,f(x)) such that x and f(x) are related by a definite...

Result used: Definition of limit: Let f(x) be a function is defined when x approaches to p then...

Statement: If n is any real number, then ddx(xn)=nxn−1. Example: Differentiate, f(x)=x2. Obtain…

Absolute maximum: A function f has an absolute maximum at c if f(c)≥f(x) ∀ x in the domain D of…

The Riemann sum of a function f is the method to find the total area underneath a curve. The area...

Thomas' Calculus (14th Edition)

Thomas' Calculus (14th Edition)

Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Function: A function is expressed in terms of dependent and independent variable. For every...

Given information: The function is g(t). The interval from t=a to t=b. Calculation: Calculate the...

Consider a function f is differentiable at a domain value a, then f′(a) is a real number. Then,…

According to the Extreme Value Theorem, If a function f(x) is continuous on a closed interval [a,...

To find the area of the shaded region R that lies above the x-axis, below the graph of y=1−x2 and...

Calculus: Early Transcendentals (3rd Edition)

Calculus: Early Transcendentals (3rd Edition)

Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Given: The given statement is “A function could have a property that f(−x)=f(x) for all x”....

Consider the rational function f(x)=x−1x2−1 (1) Take limit in the equation (1) as x approaches 1....

Explain why or why not Determine whether the following statements are true and give an explanation…

Definition used: A function f has a local maximum at a point x0 if the values f(x) of f for x…

Explain why or why not Determine whether the following statements are true and give an explanation…

Calculus: Early Transcendentals

Calculus: Early Transcendentals

Author:Jon Rogawski, Colin Adams, Robert Franzosa

Calculation: (a)2a3b which cannot be simplified further hence none of the option can be matched....

Given: s(t)=t2+1t∈[2,5] Formula used: Average velocity = Displacement ChangeTime…

Given: The graph of the function is Formula used: The average rate of change of f(x) over [a,b]…

Given: The expression is 8.113−2. Formula used: Linear Approximation: Δf=f′(a)Δx Calculation: The...

Given: The function graph is shown Formula used: L4=h∑k=03f(xk) M4=h∑k=04f(xk*) h=b−an…

Precalculus

Author:Michael Sullivan

Given: The points ( 0, 0 ), ( 4, 2 ) Formula used: Distance formula: D(P₁, P₂) = ( x 2 − x 1 ) 2 +…

Given Information: Masoud could order a pack of 8 batteries at $6.30, a pack of 16 for $13.99, a...

Given: The given equation is f(x) = 2x − 5 Formula used: For a linear function of the form f(x) =…

Given Information: The function, f(x)=4x5−3x2+5x−2 The polynomial function is in standard form of...

a. ( f ∘ g )( x ) = f( g( x ) ) = f( 1 − 2 x 2 ) = 3( 1 − 2 x 2 ) − 5 = 3(1 − 2( 2 ) 2 ) − 5 = −26

Calculus: Early Transcendental Functions

Calculus: Early Transcendental Functions

Author:Ron Larson, Bruce H. Edwards

Cengage Learning

Given: The equation, y=5x−8. Calculation: The function, y=5x−8. For x-intercept, y is equal to…

Given: The curve y=x2 and the points (1,1) and (3,9) Formula used: L(x1,x2)=∫x1x21+[f′(x)]2dx…

Given: The function, f(x)=12. Formula used: The derivative of the function,...

Given: The function f(x)=x2+5x in the interval f(x)=x2+5x. Formula used: A point c is said to be…

Given: Function is: f(x)=4x2+x+3 Formula used: Integral property as: ∫xnx=xn+1n+1+c Calculation:...

Calculus (MindTap Course List)

Calculus (MindTap Course List)

Author:Ron Larson, Bruce H. Edwards

Cengage Learning

Explanation:Given: The given equation is expressed as, y=5x−8. Calculation: The given equation…

Explanation: Given: The curve y=x2 and the points (1,1) and (3,9) Calculation: To the solve this...

Given: The given function is f(x)=12. Formula used: The derivative of the given function can be...

Explanation: Given: The function f(x)=x2+5x in the interval f(x)=x2+5x. Formula used: The point c…

Formula Used: The following integration formula holds: ∫xkdx=xk+1k+1+c Calculation: The…

Precalculus Enhanced with Graphing Utilities (7th Edition)

Precalculus Enhanced with Graphing Utilities (7th Edition)

Author:Michael Sullivan, Michael Sullivan III

Given: The points ( 0, 0 ), ( 4, 2 ) Formula used: Distance formula: D(P₁, P₂) = ( x 2 − x 1 ) 2 +…

Given: 3x − 8 = 10 Calculation: Adding 8 on both sides of the given equation 3x − 8 = 10 , we get…

Given: The given points are P = (−1, 3) and Q = (4, −2) Formula used: The distance between 2…

Given: 3 − 4x > 5 −2 > 4x − 1 2 > x x < − 1 2 Therefore the solution is { x | x < −…

Given: Calculation: a. ( g ∘ f )( −8 ) = g( f( −8 ) ) = g( 2 ) = −4

Thomas' Calculus: Early Transcendentals (14th Edition)

Thomas' Calculus: Early Transcendentals (14th Edition)

Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Function: A function is expressed in terms of dependent and independent variable. For every...

Given information: The function is g(t). The interval from t=a to t=b. Calculation: Calculate the...

Consider a function f is differentiable at a domain value a, then f′(a) is a real number. Then,…

According to the Extreme Value Theorem, If a function f(x) is continuous on a closed interval [a,...

To find the area of the shaded region R that lies above the x-axis, below the graph of y=1−x2 and...

Can't find your book?

Ask our experts your Calculus Question!

Multivariable Calculus

Multivariable Calculus

Author:James Stewart

Cengage Learning

Write the definition of the parametric curve. The parametric curve is defined as the set of…

Definition: If a sequence {an} has a limit l, then the sequence is convergent sequence, which can…

The difference between a vector and a scalar is explained in Table 1. Table 1 S No. Vector Scalar…

Vector function: The vector function is a function whose range is a set of vectors and whose…

Let the function be f(x,y) . The function of two variables is assigned by a two real numbers in…

Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Author:James Stewart

Cengage Learning

Given expression is (−3)4. Obtain the value as follows. (−3)4=(−3)×(−3)×(−3)×(−3)=9×9=81…

A function f is defined as a ordered pair (x,f(x)) such that x and f(x) are related by a definite...

Result used: Derivative rule: Let I be an interval, c∈I, and f:I→ℝ then f′(c)=limx→cf(x)−f(c)x−c...

One to one function: When a function does not takes the same value twice, then the function is...

Given: Distance between the point P from the track =1 Calculation: Two runners start at the point…

Single Variable Calculus

Single Variable Calculus

Author:James Stewart

Cengage Learning

Consider the given expression (−3)4. Since the power is 4, multiply −3 four times to compute the...

Explanation: A function f is defined as a ordered pair (x,f(x)) such that x and f(x) are related…

Explanation: Result used: Derivative rule: Let I be an interval, c∈I, and f:I→ℝ then...

Explanation: Absolute maximum: A function f has an absolute maximum at c if f(c)≥f(x) ∀ x in the...

Explanation: Given information: The function is f(x)=x2−4. The region lies between x=0 and x=3....

Precalculus: Mathematics for Calculus (Standalone Book)

Precalculus: Mathematics for Calculus (Standalone Book)

Author:James Stewart, Lothar Redlin, Saleem Watson

Natural numbers or counting numbers are the number that is simply used for calculate the object…

Given: The given functions are, f(x)=2x (1) g(x)=xx+2 (2) Calculation: The function f∘g is…

Function is a way to represent how one quantity depends on another and it can be represented by...

Calculation: The general form of a quadratic function is, f(x)=ax2+bx+c. Where, a, b and c...

The Natural exponential function with base e is f(x)=ex for all real x . On the same manner the...

Single Variable Calculus: Early Transcendentals

Single Variable Calculus: Early Transcendentals

Author:James Stewart

Cengage Learning

Consider the given expression (−3)4. Since the power is 4, multiply −3 four times to compute the...

A function f is defined as a ordered pair (x,f(x)) such that x and f(x) are related by a definite...

Result used: Definition of limit: Let f(x) be a function is defined when x approaches to p then...

Statement: If n is any real number, then ddx(xn)=nxn−1. Example: Differentiate, f(x)=x2. Obtain…

Absolute maximum: A function f has an absolute maximum at c if f(c)≥f(x) ∀ x in the domain D of…

Calculus of a Single Variable

Calculus of a Single Variable

Author:Ron Larson, Bruce H. Edwards

Cengage Learning

Given: The given equation is expressed as, y=5x−8. Calculation: The given equation is, y=5x−8.…

Given: The curve y=x2 and the points (1,1) and (3,9) Calculation: To the solve this problem we…

Given: The given function is f(x)=12. Formula used: The derivative of the given function can be...

Given: The function f(x)=x2+5x in the interval f(x)=x2+5x. Formula used: The point c is…

Formula Used: The following integration formula holds: ∫xkdx=xk+1k+1+c Calculation: The…

Calculus with Applications (11th Edition)

Calculus with Applications (11th Edition)

Author:Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Compute the percentage of 10 in 50 as follows. 1050=15=0.20 Convert the 0.20 to the percentage by...

Given: The expression 28x9y5 . Definition used: Radicals: If n is an even natural number and…

A line can have only one slope, so its slope is unique. There is no possible to get more than one...

A polynomial of degree one or less, including the zero polynomial is termed as the linear…

Rule used: Product rule: limx→a[f(x).g(x)]=[limx→af(x)].[limx→ag(x)]=A⋅B (The limit of a product…

Blitzer: Precalculus Essentials_5 (5th Edition)

Blitzer: Precalculus Essentials_5 (5th Edition)

Author:Robert F. Blitzer

Given Information: Algebraic expression 3+6(x−2)3. The value of variable x=4. Calculation:…

Given Information: The provided function is y=2x-2. Graph: Consider the provided function, y=2x-2...

Given Information: The provided expression is (8−3i)−(17−7i). Formula used: If a complex number…

Let us consider the functions are as follows: (a). f(x)=4x (b). g(x)=4−x (c). h(x)=−4−x (d)....

Given information: The radius of the circle = 6 cm Length of arc = 27 cm Formula used: (central...

Calculus: An Applied Approach (MindTap Course List)

Calculus: An Applied Approach (MindTap Course List)

Author:Ron Larson

Cengage Learning

Given Information: The provided points are (2,3), (0,6), (−5,1), (4,−3), (−3,−1). Graph: Consider...

Given Information: The provided graph is shown below, Each grid in the curve represents 1 unit by…

Given Information: The provided function. f(x)=−x2−5x+9 Formula used: To find the critical…

Given Information: The provided expression is (45)(42). Formula used: Property of exponents: For…

Given Information: The provided indefinite integral is ∫16dx. Formula used: The power rule of...

Can't find your book?

Ask our experts your Calculus Question!

Calculus and Its Applications (11th Edition)

Calculus and Its Applications (11th Edition)

Author:Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent

Given information: The graphs provided in Column B: Consider the function, y=|x| The modulus...

Consider the limit limx→−5f(x). Assume f(x)=1x−5. Therefore,…

Given Information: The statement, “A function with a relative maximum but no absolute extrema”…

Given information: The provided graphs: Consider the function, P(t)=50e0.03t At t=−40....

Given Information: The statement provided in the question is Riemann sums area way of…

Precalculus

Author:Miller, Julie, Gerken, Donna.

Mcgraw-hill Education,

It is observed that a parenthesis â€œ â€� or â€œ â€� indicates that an endpoint is not included…

Calculation: Consider two points Ax1,y1 and Bx2,y2 .Distance between two points is d , which can…

Calculation: Consider the given equation as fx=−x+52+2 . The vertex of the graph of the parabola...

Consider the function y=fx . If no horizontal line intersects the graph from the function y=fx…

Calculation: Consider the given angle, 96°28′ Convert the minute and second part into degrees. To...

Precalculus (MindTap Course List)

Precalculus (MindTap Course List)

Author:Ron Larson

Cengage Learning

Definition: Graph of linear function: A function f of the form f(x)=mx+b is called a linear...

Definition: The Remainder Theorem: If a polynomial f(x) is divided by x−k, then the remainder is...

Calculation: Given: The exponential function y=ax Now we have to graph the given exponential...

Given, The radius of the circular restaurant =47.25 feet. Time of one complete revolution of the...

Formula: Reciprocal identities: sinu=1cscu,cosu=1secu,tanu=1cotucscu=1sinu,secu=1cosu,cotu=1tanu,...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Author:Soo T. Tan

Explanation: Let P(x,y) be any point in the plane. Draw a perpendicular from P to x-axis and to...

The notation f:x→y means that f is a function from x to y where x is called the domain of the...

Explanation: Given information: The given function is N(t)=(60+2t)23 . Formula used: The power…

Explanation: If c is a constant, then ddx(c) is 0. Assume f(x)=c then use the first principal of...

Explanation: A function f is said to be increasing on an interval (a,b) if for every two numbers…

University Calculus: Early Transcendentals (4th Edition)

University Calculus: Early Transcendentals (4th Edition)

Author:Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Definition used: Horizontal-Line Test: “A function y=f(x) is one-to-one if and only if its graph...

Given information: The function is g(t). The interval from t=a to t=b. Calculation: Calculate the...

Consider a function f is differentiable at a domain value a, then f′(a) is a real number. Then,…

According to the Extreme Value Theorem, If a function f(x) is continuous on a closed interval [a,...

How can you sometimes estimate quantities like distance traveled, area, and average value with…

Precalculus (6th Edition)

Precalculus (6th Edition)

Author:Robert F. Blitzer

Given Information: Algebraic expression 3+6(x−2)3. The value of variable x=4. Calculation:…

Given Information: The provided function is y=2x-2. Graph: Consider the provided function, y=2x-2...

Given Information: The provided expression is (8−3i)−(17−7i). Formula used: If a complex number…

Let us consider the functions are as follows: (a). f(x)=4x (b). g(x)=4−x (c). h(x)=−4−x (d)....

Given information: The radius of the circle = 6 cm Length of arc = 27 cm Formula used: (central...

Finite Mathematics and Applied Calculus (MindTap Course List)

Finite Mathematics and Applied Calculus (MindTap Course List)

Author:Stefan Waner, Steven Costenoble

Cengage Learning

Given information: The given table is, Exponent Form 102=100 43=64 44=256 0.450=1 812=22 4−3=164...

Given Information: The provided graph is, Consider the provided graph of the function, To…

Given Information: The provided function is f(x)=x2+2x−3. Graph: Consider the function,…

Given Information: Amount of $6,000 is invested for 5 years at 4.75% simple annual interest.…

Given Information: The system of equations is; x+2y=42x−y=1 Graph: Consider the equations,...

Calculus & Its Applications (14th Edition)

Calculus & Its Applications (14th Edition)

Author:Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Given information: Set of real numbers, rational numbers, and irrational numbers Explanation:...

Given information: Non-vertical line Explanation: The slope of a non-vertical line is the rate of...

Given information: Describe all the important terms from the graph of functions. Explanation:…

Given information: Instructions to describe the product rule and the quotient rule. Explanation:…

Given information: Instruction to describe thelaws of exponents. Explanation: The function f ( x )…

Calculus

Author:SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Kendall Hunt Publishing

Explantion: Natural Numbers: All positive integers (other than zero) are said to be natural…

Calculation: Let the function f(x) . The limit of a function f(x) is L and L∈R , as x approaches…

A tangent to a function f(x) at the point x =a is a line that just touches the graph of the…

Given information: The absolute and relative extrema of a function. Relative extrema is the…

Given:The antiderivative. The reverese order of derivative is called antideriavtive. g...

Can't find your book?

Ask our experts your Calculus Question!

Applied Calculus

Applied Calculus

Author:Waner, Stefan.

Cengage Learning,

Given information: The given table is, Exponent Form 102=100 43=64 44=256 0.450=1 812=22 4−3=164...

Given Information: The provided graph is, Consider the provided graph of the function, To…

Given Information: The provided function is f(x)=x2+2x−3. Graph: Consider the function,…

Given information: The expression is limx→3x2−x−6x−3. Formula used: The limit limx→af(x) exists at…

Given Information: The provided function is f(x)=10x5+12x4−x+2. Formula used: Derivative of a...

Multivariable Calculus

Multivariable Calculus

Author:Ron Larson, Bruce H. Edwards

Cengage Learning

Given: P=(1,2),Q=(4,1),R=(5,4), u=PQ→,v=PR→ Formula used: If P(p1,p2) and Q(q1,q2) are the…

Given: The vector-valued function is r(t)=tanti+j+tk. Calculation: Consider the function:...

Given: The function is, f(x,y)=x2y−3 and the point is (0,4). Formula used: Given a function f(x,…

Given: The provided integral is ∫yy2xy+1dx. Formula used: The integral property of trigonometry...

Given: F(x,y,z)=xi+j+2k Formula used: ‖F(x,y,z)‖=M2+N2+P2, where...

EBK APPLIED CALCULUS, ENHANCED ETEXT

EBK APPLIED CALCULUS, ENHANCED ETEXT

JOHN WILEY+SONS,INC.-CONSIGNMENT

Given information: Domain of the function. Concept used: Domain is the set of all input numbers…

Given information: The given statement “The derivative of f at a is the instantaneous rate of…

Given: Statement as “If f(x)=5x2+1, then f′(−1)=−10 .” Formula Used: Formula of derivatives are…

Given information: The statement “The function f has a local maximum at p if f(p)≤f(x) for points…

Given information: The statement “If the velocity is positive, then the total distance traveled…

Calculus Early Transcendentals, Binder Ready Version

Calculus Early Transcendentals, Binder Ready Version

Author:Howard Anton, Irl C. Bivens, Stephen Davis

For the function f graphed in the accompanying figure, find the limit if it exists. (a) limx1fx (b)…

Explain the difference between average and instantaneous rates of change, and discuss how they are…

(a) Find dy/dx by differentiating implicitly, (b) Solve the equation for y as a function of x , and…

(a) If x1x2, what relationship must hold between fx1 and fx2 if f in increasing on an interval…

Evaluate the integrals. 12x3+4xdx

Calculus For The Life Sciences

Calculus For The Life Sciences

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Pearson Addison Wesley,

Approach: The y percentage of a number x is given by, z=xy100...(1) Here, z is the percentage…

Approach: Use concepts of radicals that break exponents in such a way that it can be taken out of...

Given: The data is given by, Year of Birth Life Expectancy (years) 1970 74.7 1975 76.6 1980 77.4...

Given: The function g(x)=xπ is an exponential function. Approach: Recall the definition of an...

Given information: The dose is 500 mg and half-life of the drug is 9 hours. Formula used: The...

Calculus (MindTap Course List)

Calculus (MindTap Course List)

Author:James Stewart

Cengage Learning

Given: 2x-1-x+5=3 Calculation: By the definition of absolute value, 2x-1=1-2x, x<122x-1, x≥12…

1) Concept: To find points P and Q we have to use concept of equilateral triangle. Sides AB and…

1) Concept: Use Closed Interval Method to find the absolute maximum and absolute minimum values…

1) Concept: The Fundamental Theorem of Calculus Fx=ddx∫0xf(t)dt then Fx=f(x) 2) Given:...

The area under the graph of f from 0 to t is the same as ∫0tfxdx. This area is given as t3 for…

Biocalculus

Author:Stewart, JAMES, Day, Troy

Cengage Learning,

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Given: A function could have a property that f(−x)=f(x) for all x . Consider the function f(x)=x2…

Consider the rational function f(x)=x−1x2−1 (1) Take limit in the equation (1) as x approaches 1....

It is known that modulus function is continuous everywhere. Therefore, the function f(x)=|2x+1|…

Definition used: A function f has a local maximum at a point x0 if the values f(x) of f for x…

Given that the functions f and f’ are continuous for all real numbers. Consider A(x)=∫axf(t)dt…

Finite Mathematics and Calculus with Applications (10th Edition)

Finite Mathematics and Calculus with Applications (10th Edition)

Author:Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

A line can have only one slope, so its slope is unique. There is no possible to get more than one...

Given: The system of equations, 2x+3y=7 (1) 5x−4y=6 (2) Calculation: Eliminate x term from…

We can graph the linear programing problem with two dimensional variables easily, but linear...

Observe that the linear programming problem consists of the objective function and the…

The given statement is, “For a particular interest rate, compound interest will accumulate faster...

Can't find your book?

Ask our experts your Calculus Question!

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Author:Michael Sullivan, Michael Sullivan III

Given information: The data below show the “zestimate”-the selling price of a home as predicted…

Given: It is provided in the problem that the relation of the sets is { ( −1, 0 ), ( 2, 3 ), ( 4,…

Given information: The linear function is f(x)=2x−5. Explanation: Let us consider the function,...

Given Information: The function, f(x)=4x5−3x2+5x−2 The polynomial function is in standard form of...

Given Information: The figure given is Calculation: From the graph we get, f(−8)=2 and g(−8)=−2...

Precalculus: A Unit Circle Approach (3rd Edition)

Precalculus: A Unit Circle Approach (3rd Edition)

Author:J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek

Given information: (0,5) is the midpoint of the line segment joining (−3,1) and (3,11). Concept...

Given: y=(x−1)2+2 Concept used: The vertex form standard equation of the parabola is y=a(x−h)2+k…

Given: The given statement is: “The function f(x)=ax is exponential if a>0 .” Calculation: The...

Given information: The angle is 240°. Graph: Consider, 240°. Since, 240°=180°+60°. So, 240° angle…

Given: sinθ=−23 and cosθ<0 Concept used: Signs of value of the six trigonometric ratios in...

CALCULUS (CLOTH)

CALCULUS (CLOTH)

Author:Rogawski

Calculation: (a)2a3b which cannot be simplified further hence none of the option can be matched....

Given: s(t)=t2+1t∈[2,5] Formula used: Average velocity = Displacement ChangeTime…

Given: The graph of the function is Formula used: The average rate of change of f(x) over [a,b]…

Given: The expression is 8.113−2. Formula used: Linear Approximation: Δf=f′(a)Δx Calculation: The...

Given: The function graph is shown Formula used: L4=h∑k=03f(xk) M4=h∑k=04f(xk*) h=b−an…

Calculus: Early Transcendental Functions (MindTap Course List)

Calculus: Early Transcendental Functions (MindTap Course List)

Author:Ron Larson, Bruce H. Edwards

Cengage Learning

Given: y=−32x+3 Linear equation of the form y=mx+b with slope m and intercept b has a graph of...

Given: The equation, y=5x−8. Calculation: The function, y=5x−8. For x-intercept, y is equal to…

Given: The curve y=x2 and the points (1,1) and (3,9) Formula used: L(x1,x2)=∫x1x21+[f′(x)]2dx…

Given: The function, f(x)=12. Formula used: The derivative of the function,...

Given: The function f(x)=x2+5x in the interval f(x)=x2+5x. Formula used: A point c is said to be…

Single Variable Calculus: Early Transcendentals, Volume I

Single Variable Calculus: Early Transcendentals, Volume I

Author:James Stewart

Cengage Learning

Consider the given expression (−3)4. Since the power is 4, multiply −3 four times to compute the...

A function f is defined as a ordered pair (x,f(x)) such that x and f(x) are related by a definite...

Given: The function is, y=x2−2x+2. Graph: Express the given function as follows....

Definition used: Logarithmic function A function such as y=logax or y=lnx that is inverse of an...

Result used: Definition of limit: Let f(x) be a function is defined when x approaches to p then...

University Calculus: Early Transcendentals (3rd Edition)

University Calculus: Early Transcendentals (3rd Edition)

Author:Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Definition used: Horizontal-Line Test: “A function y=f(x) is one-to-one if and only if its graph...

Given information: The function is g(t). The interval from t=a to t=b. Calculation: Calculate the...

Consider a function f is differentiable at a domain value a, then f′(a) is a real number. Then,…

According to the Extreme Value Theorem, If a function f(x) is continuous on a closed interval [a,...

How can you sometimes estimate quantities like distance traveled, area, and average value with…

Calculus

Author:Ron Larson, Bruce H. Edwards

Cengage Learning

Explanation:Given: The given equation is expressed as, y=5x−8. Calculation: The given equation…

Explanation: Given: The curve y=x2 and the points (1,1) and (3,9) Calculation: To the solve this...

Given: The given function is f(x)=12. Formula used: The derivative of the given function can be...

Explanation: Given: The function f(x)=x2+5x in the interval f(x)=x2+5x. Formula used: The point c…

Given: The given integral is ∫(x−6)dx. Formula used: The integral formula is: ∫xndx=xn+1n+1+C…

Study Guide for Stewart's Multivariable Calculus, 8th

Study Guide for Stewart's Multivariable Calculus, 8th

Author:Stewart, James

Given: The options are, a) parabola, b) ellipse, c) hyperbola and d) not enough information is...

Result used: The Taylor polynomial of degree n for f about a is,...

The given equation is x225+1=z216−y29. It can be rewritten as follows....

Given that, the position of the given particle at the time t is r(t)=3t3i+lntj−sin2tk. Obtain the...

Definition used: If f(x,y) and g(x,y) have continuous partial derivatives and (a,b) is a local...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Author:Stewart, James, St. Andre, Richard

Cengage Learning

Result used: “A function f is one-to-one means that for all x1,x2 in the domain of f, if x1≠x2,…

The derivative of y=f(x) with respect to x is f′(x)=limh→0f(x+h)−f(x)h. The function is...

Check whether the value of sinhx=ex+e−x2 is true or not as follows. It is known that...

The given statement is, “If h′(x)=k(x), then k(x) is an antiderivative of h(x)”. Equivalently if...

Formula used: Substitution rule: If u=g(x) is differentiable function whose range is an interval…

Can't find your book?

Ask our experts your Calculus Question!

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Author:Soo T. Tan

Cengage Learning

Result used: Laws of Exponents: For any real numbers a, b and n(ab)n=anbn,(b≠0). Calculation: The...

Let P(x,y) be any point in the plane. Draw a perpendicular from P to x-axis and to y-axis, then x…

The notation f:x→y means that f is a function from x to y where x is called the domain of the...

If c is a constant, then ddx(c) is 0. Assume f(x)=c then use the first principal of derivative....

A function f is said to be increasing on an interval (a,b) if for every two numbers x1 and x2 in…

Calculus

Author:Laura Taalman, Peter Kohn

If the values of a function approach as approaches then we say that is the limit of as approaches...

Given:Tangent line and secant line Concept used:tangent line gives a slope of the equation and...

Given information: “The function f has a local maximum or a local minimum at x=c ”. The function…

Given information: Consider the function f over an interval [a,b]. Generally, the Riemann sum is…

Calculus : The Classic Edition (with Make the Grade and Infotrac)

Calculus : The Classic Edition (with Make the Grade and Infotrac)

Author:Earl W. Swokowski

Given: The given expression is (−5)|3−6| Calculation: The absolute value |a| of a real number ‘a’...

Given: f(x)=x−4−3x Calculation: Substituting x = 4 in f(x) , we get f(4)=4−4−3(4)=−12 Substituting…

Given: 150∘ Concept Used: 1. To change radian measure to degrees, multiply by 180π 2. To change...

Given: limx→−2(3x−1) Calculation: limx→−2(3x−1)=3⋅(−2)−1 (Replace x by −2)=−6−1=−7 Conclusion:...

Given information: The limit limt→cv(t)=k Consider the limit limt→cv(t)=k The above equation can…

University Calculus

University Calculus

Author:Joel R. Hass, Maurice D. Weir, George B. Thomas, Jr., Przemyslaw Bogacki

Calculus: Early Transcendentals (2nd Edition)

Calculus: Early Transcendentals (2nd Edition)

Author:William L. Briggs, Lyle Cochran, Bernard Gillett

Given: The given statement is “A function could have a property that f(−x)=f(x) for all x”....

Consider the rational function f(x)=x−1x2−1 (1) Take limit in the equation (1) as x approaches 1....

Explain why or why not Determine whether the following statements are true and give an explanation…

Definition used: A function f has a local maximum at a point x0 if the values f(x) of f for x…

Explain why or why not Determine whether the following statements are true and give an explanation…

Calculus: Early Transcendentals

Calculus: Early Transcendentals

Author:Jon Rogawski, Colin Adams

The absolute value, also defined as modulus |x|, of any real number x, is referred to as the...

Given: s(t)=t2+1t∈[2,5] Formula used: Average velocity = Displacement ChangeTime…

Given: The graph of the function is Formula used: The average rate of change of f(x) over [a,b]…

Given: The expression is 8.113−2. Formula used: Linear Approximation: Δf=f′(a)Δx Calculation: The...

Given: The function graph is shown Formula used: L4=h∑k=03f(xk) M4=h∑k=04f(xk*) h=b−an…

Precalculus (10th Edition)

Precalculus (10th Edition)

Author:Michael Sullivan

Given: The points ( 0, 0 ), ( 4, 2 ) Formula used: Distance formula: D(P₁, P₂) = ( x 2 − x 1 ) 2 +…

Given: It is provided in the problem that the relation of the sets is { ( −1, 0 ), ( 2, 3 ), ( 4,…

Given: The given equation is f(x) = 2x − 5 Formula used: For a linear function of the form f(x) =…

Given Information: The function, f(x)=4x5−3x2+5x−2 The polynomial function is in standard form of...

a. ( f ∘ g )( x ) = f( g( x ) ) = f( 1 − 2 x 2 ) = 3( 1 − 2 x 2 ) − 5 = 3(1 − 2( 2 ) 2 ) − 5 = −26

Calculus: Single And Multivariable

Calculus: Single And Multivariable

Author:Hughes-Hallett, Deborah; Mccallum, William G.; Gleason, Andrew M.; Connally, Eric; Kalaycioglu, Selin; Flath, Daniel E.; Lahme, Brigitte; Lomen, David O.; Lock, Patti Frazer; Lovelock, David; Morris, Jerry; Lozano, Guadalupe I.; Mumford, David; Quinney, D

Find formulas for the functions described in Exercises 18. A line with slope 2 and x-intercept 5.

At time t in seconds, a particles distance s(t), in cm, from a point is given in the table. What is…

Find derivatives for the functions in Exercises 173. Assume a, b, c, and k are constants. w = (t2 +…

For Exercises 12, indicate all critical points on the given graphs. Which correspond to local…

Can't find your book?

Ask our experts your Calculus Question!