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Q: Evaluate the difinite integral. ∫12x3lnx4dx type an exact answer in simplified form.

A: We need to compute the value of the given integral,

Q: Find the derivative.

A: Given function is

Q: If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

A: Given,

Q: Find the particular solution of the differential equation dy/dx+ycos(x)=4cos(x) satisfying the initi...

A: Given differential equation is,

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at whic...

A: Given,Surface area is decreasing at rate = 3 cm2 per minDiameter of the snowball (d) = 11 cm

Q: Find the integral of x^2 * cos(4x) dx.

A: To compute the indefinite integral.

Q: Find all critical points of the function f(x) 3x + 12x + 11. (Use symbolic notation and fractions wh...

A: |2x + 1| = 2x + 1 if 2x + 1 ≥ 0 i.e. x ≥ -1/2|2x + 1| = -(2x + 1) if 2x + 1 < 0 i.e. x > -1/...

Q: Answer the following questions about the function whose derivative is f′(x)=x2(x-3)/x+6. Assume the ...

A: To determine:Part a) The interval of increasing and decreasing f.Part b) The local maximum and minim...

Q: Can you help me step by step?

A: Given: -

Q: The marketing division of a large firm has found that it can model the sales generated by an adverti...

A: Given,

Q: show that the given function is one-to-one and find its inverse. Check your answersalgebraically and...

A: Given:

Q: Find the derivative using the following information.

A: Equation of tangent to curve g(x) at x=2 is y=-3x+2. Its slope is m=-3. Since slope of tangent to cu...

Q: Evaluate the integral dx/2sqr(x+3)+x

A: Given that

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one inpu...

A: Given,

Q: Find the derivative h(x)= sin(tan 2x)

A: Given,

Q: How do you solve this? I got -6 and 3 and it said it was incorrect, I also tried -3 and 6 but it was...

A: Given,

Q: For the given function, find all values of cover the interval (4, 8) stipulated by Rolle's Theorem s...

A: Given function in interval (4, 8)

Q: cos(2 tan−1(x))

A: Given,

Q: Q 7. Is cos x| differentiable in (-oo, oo). If so find its derivative. If not, is it differentiable ...

A: Let us begin with plotting the graph for |cos x|.

Q: 3.3 Can you show me the steps to solve the problem? Directions: (a) Find the intervals of increase o...

A: to determine the function increasing.

Q: Calculus Question

A: Given:

Q: Calculus Question

A: Dividing by highest denominator power ie by x

Q: How do you solve this?

A: Click to see the answer

Q: 4. Let f(x talk about its inverse.) Without finding a formula for f1(x), find (f1)'(4) Vx26 (We rest...

A: To determine (f-1)’ (4) without using formula of inverse.

Q: Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above...

A: Given, barometric pressure function is

Q: For the composite function, identify an inside function and an outside function and write the deriva...

A: Plug f(x)= g(h(x)) in the given function.

Q: lo eTTIoprvars ruc, -too 42 3r (c) Use the substitution rule to show that lim0 f(x) = lim^0+ f() and...

A: Given

Q: Can you help with this problem step by step?

A: Given,

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) e9x e~x (a) Find the int...

A: NOTE: As you have posted a question with multiple subparts, we will answer the first subpart as per ...

Q: How do you solve this?

A: To find the roots of the given polynomial equation

Q: Find a formula for the sum of n terms. Use the formula to find the limit as n → ∞.

A: Formula:

Q: 1 0 -1 1. For what values of x does the function f have a local maximum on (0,8)? Answer (separate b...

A: Functions can have "hills and valleys": places where they reach a minimum or maximum value. It may n...

Q: Find the following indefinite integrals. X dx= Vx6 +C

A: Given,

Q: 2. If you graph the function 1 - el/ x f(x) 1+el/x you will see that f appears to be an odd function...

A: Recall the following fact.

Q: An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at...

A: Model the given problem as follows.

Q: How do you find an equation of a line given a pair of points? EX: (22,26), (4,8)

A: Finding an equation of a line by giving two points

Q: Differentiate the function g(x) = ln(xe-2x).

A: Given function is,

Q: see attachment

A: For the polar coordinates,

Q: Use a graph of to estimate the maximum and minimum values. Then find the exact values. Estimate th...

A: Please see the graph on white board. The maxima is infinity and minima is 0.

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Click to see the answer

Q: Answer the following questions about the function whose derivative is f′(x)=(x+2)e^-x.Assume the do...

A: for increasing and decreasing the function.

Q: 0 and f" (x) < 0 for all x 50. Suppose f(3) = 2, f'(3) and f'(x) 2 a. Sketch a possible graph for f ...

A: We can conclude from f(3) = 2 that the value of f(x) at x = 3 is 2.So we got one point on the curve ...

Q: see attachment

A: The relation between the temperature and the height above a distance planet is,

Q: Find the intervals of increase or decrease. Find the local maximum and minimum values. Find the ...

A: Given:

Q: The marketing division of a large firm has found that it can model the sales generated by an adverti...

A: From the given information, it is observed that the aim is to find the ds/dx at the point x = 12.

Q: Find an equation for the line tangent to the graph of f(x)=−7xe^x at the point (a,f(a)) for a=2.

A: Given:

Q: The average length of the outer ear for men can be modeled as f(x)0.89 0.495 In x inches a s 70.T wh...

A: Find f (x(15)) as follows.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y=x3, 0<x<...

A: If the curve y = f(x), a ≤ x ≤ b is revolved about the x-axis, then the area of the resulting surfac...

Q: How do you get the derivative of (6-18x^2)/((1+3x^2)^2)?

A: Given function is

Q: how do you indicate the derivative with any method: g(t) = 3/t^5; estimate g'(1)

A: Write g(t) using negative exponents to get rid of the fraction. Then use exponent rule. d/dx(x^n)=n*...