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Q: Let f(x)=ex2. It can be shown by direct computation that f(4)(x)≤76e on the interval [0, 1]. Using t...

A: Compute the first, second and third derivative of the given function as follows.

Q: 7. According to a simplified economic model, the purchasing power of 1 dollar in the 2000t is equal ...

A: 2000+t=2020So, 20 years.

Q: A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y=16-...

A: Please see the white board. The rectangle is represented by the green line.The inverted parabola is ...

Q: indefinite integral of x7/8 dx

A: Given integral is

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

A: To find critical points we set f'(x)=0 and solve for x. Answer(a): -5,5

Q: Evaluate the integral -2t sin(-3t) dt Note: Use an upper-case "C" for the constant of integration.

A: Given Integral;

Q: Evaluate the following limits. If needed, enter INF for oo and MINF for -oo. (a) -)= x 5x1- x lim (b...

A: Evaluate the following limit,

Q: Find the area of the surface generated when the curve f(x) = (2/3)x^(3/2) - (1/2)x^(1/2) ; [1,9] is ...

A: Given:

Q: Use integration by parts to evaluate the integral. 6 3 e cos x dk 0

A: The given integral is,

Q: see attachment

A: Domain and range of sec(x) are

Q: The height (in feet) of a certain kind of tree is approximated by h(t)= 120/1+180e-.34t where t is t...

A: The height of a tree in feet as a function of time t in years is as follow:

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: 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: Analytically, what is the slsmt symptote of the following function. Please shoiws alll math.

A: Given function is

Q: step by step please f(x)=a(b)x the x at the end of that formula is an exponent of b , i believe

A: Substitute given two points to solve for a and b.

Q: see attachment

A: For a function of the form y=A sin(B(x+C))+D, amplitude is A, period is 2pi/B,phase shift is C.So we...

Q: A silo (base not included) is to be constructed in the form of a cylider surmounted by a hemisphere....

A: Click to see the answer

Q: The question says: "A pair of paraetric equations is given. a.) Sketch the curve represented by the ...

A: To sketch the graph, the points (x, y) are to be determined for different t values and then the poin...

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

A: First, here we will use the graph of the function to estimate the maximum and minimum values.

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line tange...

A: Slope of tangent line is ½. So the equation is of the form:

Q: For arbitray values of K and b, when does the maximum growth rate occur (in terms of K and b)? P(t)=...

A: Compute first derivative as follows.

Q: Can you help me on #1

A: Distribute secx use 1/secx=cos xThen simplify.

Q: Find the area of the region enclosed by one loop of the curve. r=sin(8theta)

A: Draw the given curve as shown below.

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

A: Given function is

Q: Find the derivative using the following information.

A: Given,

Q: Find the derivative of y with respect to x. y= csc^-1 (x^2+1) , x>0

A: Given ,

Q: find the critical points, points of inflection, local maxima and minima and graph the function:

A: Given,

Q: Find h(-2) h(t)=t^2-4t+2

A: The given function, h is,

Q: If f'(1) = 1, f(2) = 3, f'(2) = -3, f'(4) = 10, g(1)= 4, g'(1) = 2, find (f o g)'(1) and (f(xg(x)))'...

A: Apply chain rule on to find (fog)'(1)then plug the given values. Answer: (fog)'(1) = 20

Q: Make an appropriate substitution and then use integration by parts to evaluate the integral. sin x 6...

A: Given integral is

Q: For what value of k will y=2x^2+kx-9 have a minum at x=3?

A: The given equation is,

Q: Which of the following functions are solutions of the differential equation y′′−9y′+18y=0?A. y(x)=e3...

A: The given differential equation is,

Q: A piece of wire of length 63 is cut, and the resulting tow pieces are formed to make a circle and a ...

A: The total length of the wire is 63.Let x be the length of the wire cut for the circle.Then, 63-x is ...

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

A: The given composite function is,

Q: For number 3, how to find radius and height? And how do I know for height which function to subtract...

A: Given thatGiven that

Q: The world's output of primary energy (petroleum, natural gas, coal, hydroelectricity, and nuclear el...

A: It is increasing at the rate of 2.4% annually. So 0.024 every year.growth rate= (1+0.024)=1.024 per ...

Q: In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Fr...

A: Observe the given facts as follows.

Q: Determine if the series below converges or diverges. Show all steps in whichever test you use. If a ...

A: Click to see the answer

Q: Use the method of partial fraction decomposition to perform the required integration X3 dx (x-7)2 X+...

A: to 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: What is the moment of inertia about the origin

A: Definition: Given a plane object on the region D with continuous density p(x,y) , the moment of iner...

Q: sin ba +sin cxsin dx = 4 ar lim0 Find the Q 8. a, b, c, d are constants such that 3a2547x6 0.) value...

A: The given limit is,

Q: Use integration by parts to evaluate the integral. ∫0π/3 5exsinx dx type an exact answer

A: Given, definite integration is

Q: Write the equation in spherical coordinates. 2x2 - 3х + 2y2+ 22? (a) = 0 3p(p sin(p)cos (0)) 2 2х + ...

A: Consider the following spherical coordinates.

Q: Find the limit as x approaches infinity of f(x) when f(x) is x times square root of x

A: x times sqrt(x)= x times x^(1/2)= x^[1+1/2] = x^(3/2)

Q: An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a...

A: Assume that side of square which should be cut from each corner is a.Given the dimension of piece of...

Q: find the absolute extrema for f(x) = x^2/3 (2-x) on [-1,2] I know the critical points are 4/5 and ...

A: compute the critical points as follows.

Q: 2. Microtutorial eled by the equation The Pacific halibut fishery has been mod- 8 x 107 B(t) 11 1 +3...

A: Given function

Q: Suppose an initial population of 33 million people increases at a continuous percent rate of 1.8% pe...

A: Initial population in year 2000

Q: The function f has a continuous second derivative, and it satisfies f(7)=5, f′(7)=4 and f″(7)=−2. We...

A: f"(7)=-2 Since f " (7) < 0 so at x=7 f(x) is concave down.