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Q: Find the derivative.

A: Given,

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: An oil drilling rig located 14 miles off of a straight coastline is to be connected by a pipeline to...

A: Click to see the answer

Q: A model for growth of a sandwich shop franchise is N(t)=-765+482lnt where N(t) is the number of loca...

A: Given:

Q: Find the derivative

A: To compute the derivative of the given function (involving exponentials)

Q: Consider the sequence 4, 11, 18, 25, 32, .... a. Is 340 a member of the sequence? b. Is 738 a member...

A: It can be observed that the given sequence has a constant difference of 7 between the successive ter...

Q: Find the area of the region enclosed by one loop of the curve. 18. r^2 = 4cos2(theta)

A: Refer to the question we need to find the area of the region enclosed by one loop of the curve.

Q: Optimization: You and your classmates have decided to enter an ice sculpting contest. Before you beg...

A: Given an ice block with the following conditions,

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: Solve the indefinite integral:

A: Given:

Q: if sin(0)=-7/25 with 0 quadrant IV, what is cos(0)?

A: Given

Q: What does the nth term test determine for the summation of (e^n)/(e^n+n) from 0 to infinity?

A: We are given the expression,

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: 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: Can you help me on #27

A: The series1/k2 converges. We compare given series to this series and use comparison test.

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: Evaluate the indefinite integral -10 sin (x) cos(x) dx +C

A: Given:

Q: Approximate the integral from 2 to 14 (x2 -5)dx using 4 rectangles

A: To find the area under the curve using rectangles, the Reimann sum is used.First, we need to find th...

Q: Find the derivative of the function f(x)= e^-3x ln x

A: Given function is

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

A: (a) Finding the local extremas:

Q: Calculus Question

A: Dividing by highest denominator power ie by x

Q: Find the area of the largest rectangle that can be inscribed in an equilateral triangle of side leng...

A: To determine the rectangle which give the maximum area under the given conditions

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

A: You have asked a question with multiple sub parts. I will address the first three sub parts. Please ...

Q: Finding derivative.

A: Given,

Q: A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 40...

A: Consider the given information about water trough:

Q: how to solve problem in photo attached

A: The given integral is,

Q: how to solve problem in photo attached

A: Given:

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

A: Given,

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: Use partial fraction decomposition to evaluate the integral. ∫6x2-13x+3/x2(x-3) dx

A: Refer to the question we need to find the integration using partial fraction for the provided integr...

Q: How do you find the spherical coordinates of the following problem?

A: Given, Triple integral is

Q: Find the absolute minimum and absolute maximum values of f on the given interval 2sin2t after differ...

A: Given function is

Q: Find an equation of the tangent line to the graph of y = e−x^2 at the point (4, 1/e16).

A: Slope of tangent line is equal to value of the first derivative of y at given point.

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

A: Given, definite integration is

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: see attachment

A: Click to see the answer

Q: Find the intervals on which is increasing or decreasing. Find the local maximum and minimum values...

A: Refer to the question , we have been provided with the function , f(x) = cos2x-2sinx, 0<=x<=2p...

Q: The number of online buyers in Western Europe is expected to grow steadily in the coming years. The ...

A: (a) The percentage of online buyers in the year 2001 is evaluated as follows.

Q: For the solids of revolution, how do I know when to add or subtract from the axis of revolution such...

A: For the solids of revolution, find the volume using disk, washer and cylindrical shell method.

Q: Problem 1 Parts 1, 2, and 3

A: To determine:Part 1) Approximate value of f(3.01) using linear approximation.Part 2) The actual valu...

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.

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: Optimization: A family wants to build a fence in their backyard for their dogs. If they can only aff...

A: Click to see the answer

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

A: The given equation is,

Q: Differentiate the function F(t) = (ln t)2 sin t

A: Given function is,

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: Sketch the graph of a function that satisfies the following 3. conditions: (a) f'(0) f'(2) = f'(4) =...

A: There are many ways to draw the graph. From part (a), observed that the function has local minimum o...

Q: Differentiate. y = (4-sec x)/tan x

A: Distribute tan x.1/tanx= cot x and secx/tanx= cscx

Q: An open-top crate is to be constructed with 54 ft2 of material available to use. The length of its b...

A: Let width = x So, length = 2xLet height = hVolume of the crate = V = (x)(2x)(h)= 2hx^2

Q: A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it...

A: Let length of the sides are x and y. And the middle fence is parallel to x side.So total fence neede...