if x < 1 -{ f(x) ! if x > 1 fωα f(x) dæ

Q: What is an exponential function? Give examples. What laws of exponents does it obey? How does it dif...

A: To describe the exponential function, law of exponents, describe the difference between exponential ...

Q: use logarithmic differentiation to find the derivative of y with respect to the given independent va...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Observers at positions A and B 2 km apart simultaneously measure the angle of elevation of a weather...

A: Given that at positions A and B, 2 km apart simultaneously measure the angle of elevation of a weath...

Q: Suppose that the dollar cost of producing x washing machines is c(x) = 2000 + 100x - 0.1x2. a. Find ...

A: Consider the given cost function.

Q: What is the number e, and how is it defined? What are the domain and range of ƒ(x) = ex? What does i...

A: The base of natural logarithm is the number e and it is a constant whose value is approximately equa...

Q: Exercise 7: Compute the derivative (with respect to x) of the following functions, using the first f...

A: Hello, thanks for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3. Pl...

Q: Radioactive decay The half-life of phosphorus-32 is about 14 days. There are 6.6 grams present initi...

A: Given:Radioactive decay the half-life of phosphorus-32 is about 14 days. There are 6.6 grams present...

Q: Find equations of all lines having slope -1 that are tangent to the curve y = 1/(x - 1).

A:

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other...

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x, 

Q: find dy/dx. 1. ln y = e^y sin x    2. x^y= y^x

A: 1) Given thatln y = ey sinx        …(1)

Q: In Exercises 19–22, find the slope of the curve at the point indicated.    19. y = 5x - 3x2, x = 1  ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: What is one way of expressing the special number e as a limit? What is an approximate numerical valu...

A: To determine the limit representation of the exponential function and numerical value of e to 7 deci...

Q: How can you write any real power of x as a power of e? Are there any restrictions on x? How does thi...

A: Consider the number xa.The number xa can be expressed as a power of e as shown below.

Q: The function ƒ(x) = |x| has an absolute minimum value at x = 0 even though ƒ is not differen-tiable ...

A:

Q: Let ƒ(x) = ax + b and g(x) = cx + d. What condition must be satisfied by the constants a, b, c, d in...

A: Given: ƒ(x) = ax + b and g(x) = cx + d

Q: Hello, I need help with part f. thank you

A: Consider the given integral:

Q: If x moves from a to a nearby value a + dx, how do you estimate the corresponding change in the valu...

A: First of all, consider a differential function f (x).Consider two points a and a + dx on x axis.The ...

Q: Show how to extend the functions in Exercises 133 and 134 to be continuous at the origin. 133. g(x) ...

A:

Q: Sketch the graph y = 2 cos (x -pai/3)

A: The given function is,

Q: Find the linearizations of    a. tan x at x = -pai/4  b. sec x at x = -pai/4. Graph the curves and l...

A: Linearization of a function f(x) at a point a is defined by

Q: 7. Find the derivate of the following, i.e. Find y 2In(r)tcotfe)

A: Given:

Q: Does knowing that a function ƒ(x) is differ-entiable at x = x0 tell you anything about the different...

A: Given:Does knowing that a function ƒ(x) is differentiable at x = x0 tell you anything about the diff...

Q: The radius of a circle is changing at the rate of -2/pai  m/sec. At what rate is the circle’s area c...

A:

Q: f(x)=x^11h(X) h(-1)=3 h'(-1)=6  calculate f'(-1)

A: Differentiate right side of f(x) using product rule.

Q: a. Graph the function ƒ(x) = sqrt(1 - x2), 0&lt;=x&lt;=1. What sym-metry does the graph have? b. Sho...

A: PART a.The function given is

Q: Radioactive decay The half-life of a certain radioactive sub-stance is 12 hours. There are 8 grams p...

A: Given, The half-life of a certain radioactive sub-stance is 12 hours. There are 8 grams present init...

Q: What is the length of the blue line labeled r in the image below? Give your answer in terms of a and...

A: The length of r is found using the following triangle ABC.

Q: g(x) = 8x2 + 40x − 13; g(x) = 819 Calculate the corresponding output or input value.

A: First of all, consider the given function g (x) and the value of g (x).Simplify the equation to get ...

Q: What role does the derivative play in defining slopes, tangent lines, and rates of change?

A: To determine the role of derivative of a function in defining slopes, tangent lines and rate of chan...

Q: What procedure can you sometimes use to express the inverse of a function of x as a function of x?

A: Consider f(x) to be a function of x.

Q: Suppose that ƒ and g are both odd functions defined on the entire real line. Which of the following ...

A: Let  ƒ and g are both odd functions defined on the entire real line. Which of the following  are eve...

Q: sec2 (2x) -d.xp 2. Evalaute tan(2x)

A: Given:

Q: Use the linear approximation (1 + x)k ≈ 1 + kx to find an approximation for the function ƒ(x) for va...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Exercise 5: The equation for the unit circle is x? + y? = 1. (a) Solve for y (assuming y is non-nega...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: The edge x of a cube is measured with an error of at most 0.5%. What is the maximum corresponding pe...

A: Given:

Q: find dy/dx by implicit differentiation.   1. x2 + xy + y2 - 5x = 2    2. 5x^(4/5) + 10y^(6/5)=15

A:

Q: What is the linearization L (x) of a function ƒ(x) at a point x = a? What is required of ƒ at a for ...

A:  linearization is finding the linear approximation to a function at a given point.It is given by,

Q: If Juanita invests $1500 in a retire-ment account that earns 8% compounded annually, how long will i...

A: Given:Juanita invests $1500 in a retirement account the earns 8% compounded annually, and the amount...

Q: Consider the following function: z = α x+ β y^2, where alpha and beta are constant parameters. Write...

A: To find the total differential dz and partial derivatives.

Q: Are there two functions ƒ and g such that ƒ ∘ g = g ∘ ƒ? Give reasons for your answer.

A: There are functions f and g such that,

Q: I dont understand how the integration by parts was done here. I was thinking they made sec^2 on purp...

A: Given:

Q: • sin ( x ) + t)dt cos(t*) h(x) = -3 h'(x) = Preview Enter an algebraic expression [more..]

A: Given,

Q: The impedance Z (ohms) in a series circuit is related to the resistance R (ohms) and reactance X (oh...

A: Given,

Q: find an equation for a circle with center (2,-1) that passes through (5,4).

A: Given a circle with center (2,-1) that passes through (5,4).

Q: Suppose that ƒ′(x) = 2x for all x. Find ƒ(2) if a. ƒ(0) = 0 b. ƒ(1) = 0 c. ƒ(-2) = 3.

A:

Q: Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following ...

A: To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are ch...

Q: The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year. Approximate...

A: Given The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year. Appro...

Q: Given that f(x)=2x−5 and g(x)=8−x2, calculate: f(g(0))=

A: Given,

Q: Va dx using upper and lower sums. Guess a (rational) number for the value of the Exercise 2: Estimat...

A: Let n be an integer. In this question let n=4  Now first find the upper sum of the integral: 

Q: Find the values of h, k, and a that make the circle (x - h)2 + (y - k)2 = a2 tangent to the parabola...

A: