Answered: f(x) = x² – 5, g(x) = Vĩ; lim(f° g)(x)

Math

Calculus

f(x) = x² – 5, g(x) = Vĩ; lim(f° g)(x)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.6: Rational Functions

Problem 2E

See similar textbooks

Related questions

Q: Q5,Q6

A: A Maclaurin series is given by f(x) = ∑k=0∞fk(0)k !xk Given function f(x) = x5 tan x Here, each...

Q: Find the derivatives of the following function f(x)

Q: Fill in the blank? The set of numbers in the form a/b, , where a and b belong to the set {….., -4, -...

Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in ...

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1 ........................(1)Given conditions...

Q: Find f + g, f - g, fg, and f/g and determine the domain for the given function : f(x) = √(x - 2), g(...

Q: Solve the equation cos2 + sin = 1 for θ, where 0 ≤ θ ≤ 2π.

Q: Find the area od the surface generated by revolving the curve y=2√x 1<=x<=2 about x-axis

Q: Explain how to factor x3 + 1.

A: To explain how to factor x3+1.

Q: Use properties of logarithms to condense the logarithmic expression, log x + log(x2 - 1) - log 7 - l...

A: We have to condense the logarithmic expression using logarithmic properties: logx+logx2-1-log7-logx+...

Q: Find the integral ∫(x3 + x)5(3x2 + 1) dx.

A: we have to find the integral of ∫(x3 + x)5(3x2 + 1) dx.

Q: Working with parametric equations Consider the following parametric equations.a. Eliminate the param...

A: Given, x = 3 + t, y = 1 - t; 0 ≤ t ≤ 1 part a: x=3+t⇒t=x-3 We have, y=1-t Therefore, ⇒y=1-x+3⇒y=-x+4...

Q: Show that the sum of the squares of the direction cosines of a line through the origin is equal to 1...

A: To show: The sum of the squares of the direction cosine of a line through the origin is equal to 1.

Q: Find the Taylor polynomials p3 and p4 centered at a = 0 for ƒ(x) = (1 + x)-3.

A: Given that: The function f (x) = ( 1+x) - 3 .

Q: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?

A: We have to explain What happens to the rate of change of the logarithmic function y = loga x as a be...

Q: find the limit or explain why it does not exist

A: Let the given limit be y - y = limh→0 x+h2-x2hy = limh→0 x2+h2+2xh-x2h ...

Q: Suppose that the marginal propensity to consume is dc e-0.5y (in billions of dollars) dy and that co...

Q: Evaluate the trigonometric function cos π at the quadrantal angle, or state that the expression is u...

A: Since θ is π, the terminal side of the angle is on the negative x-axis. We can select the poi...

Q: find the derivative of y with respect to the appropriatevariable. y = sin-1√2 t

A: To find the derivative of y=sin-12t

Q: 35. /2.1 – V2 is larger than /9.1 – ỹ.

Q: Solve quadratic equation. x2 = 6x - 7

A: Given x2 = 6x - 7. We need to solve the quadratic equation.

Q: Find the area between the curve y = 2(ln x)/x and the x-axisfrom x = 1 to x = e.

A: Consider the given: y=2lnxxandy=0Interval 1,eFind the area:A=∫1e2lnxx-0dxA=∫1e2lnxxdx

Q: Evaluate the integral.

A: Given: The integral, ∫12x5lnx dx.

Q: Why is the logarithmic function not defined for negative values of x, thesoftware can produce only...

A: The definition of logarithmic function is, logbx=y⇒by=x The output value of exponential function by ...

Q: Use integration to find the general solution to the differential equation. (Use C for the constant o...

Q: Please solve part D.

Q: Cost, revenue, and profit are in dollars and x is the number of units. If the marginal cost for a pr...

A: Given: Marginal cost MC=130+0.15x. Total cost of producing 100 units are TC=45000. Marginal cost i...

Q: Find the partial fraction decomposition of (4x2 + 5x - 9)/(x3 - 6x - 9)

Q: Absolute extreme values Find the absolute maximum and minimum valuesof the following functions.a. ƒ(...

A: Find the absolute maximum and minimum: fx=x4−2x3f'x=4x3−6x2Substitute f'x=0,4x3−6x2=02x22x−3=0x=0, x...

Q: Fill in the blank/s : A triangle with one angle measuring 90° is called a/an .................. tria...

A: A triangle with one angle measuring 90° is called a/an _______ triangle. The side opposite the 90° a...

Q: Evaluate the expression log1717 without using a calculator. If evaluation is not possible, state the...

Q: Assume each plane flies horizontally in a crosswind that blows horizontally. An airplane flies east ...

A: a. Find the velocity of the plane relative to the air va, the velocityof the crosswind w, and the ve...

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫z(ln z)2 dz

A: Since, we have to evaluate the integral given below:-∫z(ln z)2dz -(i) using substitution and integra...

Q: Fill in the blank/s : x/5 ÷ x/3 = ............, x ≠ 0..

A: The given expression (division) is: x5÷x3 The replace division symbol with multiplication symbol, mu...

Q: Consider the following. 2y dx – x dy = 2 dx Solve for dy dx dy dx Is y - 3x2 + 1 a solution to 2y dx...

A: We have, 2ydx-xdy=2dxxdy=2ydx-2dxxdy=(2y-2)dx

Q: Sketch a graph of a function whose derivative is always negative. Explain how you found the answer.

A: Sketch a graph of a function whose derivative is always negative. Explain how you found the answer.

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm, g(x...

A: limx→∞lnx3x=limx→∞3lnx2·1x1 By using L'Hospital's rule=limx→∞3lnx2x=limx→∞3·2lnx·1x1 By using ...

Q: How do you determine the absolute maximum and minimum valuesof a continuous function on a closed int...

A: Let f be a continuous function in a closed interval a,b. We will Evaluate f at all the critical poin...

Q: Let z be a function of x and y, while x and y are functions of t. Explain how to find dz/dt.

A: Let z be a function of x and y, while x and y are functions of t. Then, dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: Find dy/dx x = t2 , y = 7 − 6t

A: Given that: The parametric equations, x = t2 y = 7 - 6t

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Use the equations for the shown functions f and g to graph the function y = ( f ∘ g)(x). Then use the graph of f ∘ g to find the indicated limit.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=
True or False? For every solution x(t) of the equation x′′−x′+x = 0 the equality lim t→∞ x(t) = 0 holds.
Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find the equation of the line tangent to the graph of ff at x=2. y=?
lim y approaches 0 ................... [5y3 + 8y2]/[3y4 - 16y2]
In the function: f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?
For f(x) = the square root of 7x+30, how can I find f’(x) using the definition f’(x) = lim as h—>0 (f(x+h)-f(x))/h f’(x)= ? y= ?
1. Find the dy/dx using logarithmic differentiation y=(x2(x4+5)1/2)/(ex-x^4) 2. Find the limit lim x->∞ ((8x3+x2)1/3-2x)
Let f(x)= 1/(3x+2) find the values below 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4) Find the equation of the line tangent to the graph of f at x=2. y=?
For every solution y(x) of the equation y''+ 2y'+ 5y = 0 it is true that limx→∞ y(x) = 0. ?
What is the minimum value of F(x) = -4 sin x? -4 -2 -1
Let f(x)= √6-x . Compute f'(2) using the limit definition. f'(2)= -1/4 Find an equation of the tangent line at x=2 y= ? How to solve for the equation of the tangent line at x=2?
Solve for A and B so that F(x) has a limit at both x=2 and x=4