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CalculusQ&A LibraryPrevious Problem List Next (1 point) For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential function f (that is, Vf- F). If it is not conservative, type N f (r,y)- f(r,y)- f(, y,z) f (r,y)- f(r, y,a Note: Your answers should be either expressions of x, y and z (e.g.-3xy + 2yz''), or the letter' N'Start your trial now! First week only $4.99!*arrow_forward*

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Q: 3 dx = 1 2x 8 In 국 5 -4 In 2 In을 -2 In -8 In LOn LOn

A: Obtain the value of the integral as follows.The given integral is,

Q: using the formula attached to this question find the GINI Index if the Lorenz Function is Y= 0.92x1....

A: The given Lorenz function is,

Q: Consider an object moving along a line given the velocity v. Assume t is time measured in seconds an...

A: To find the direction we have to graph the function v(t)=2t^2-16t+24;[0,7]And then we check the inte...

Q: Find the function which solves the initial value problem dy/dx= 3ex −2x; y(0)=−1.

A: Given that dy/dx = 3ex-2x; y(0) = 1.dy = (3ex-2x)dx (By cross multiplying)Integrate on ...

Q: The rate at which blood pressure decreases in the aorta of a normal adult after a hearbeat is dp/dt=...

A: It is given that rate at which the blood pressure decreases in the normal adult is dp/dt=–46.645e–0....

Q: Is y=e6x −3x−2 a solution to the differential equation shown below? y′−6y=7x+3

A: Here given differential equation is:Find the solution of given differential equation and match the g...

Q: Let H(x)=4f(x) + 5g(x), where the graphs of f and g are shown in the figure. Find H`(1).

A: Firstly, we find the function y=f(x) , which is linear function , as it is a equation of straight ...

Q: Kindly help

A: The Taylor series can be obtain as follows.

Q: Find the relative maxima, relative minima, and points of inflection and sketch the graph for the fun...

A: We have to find the relative maxima, relative minima, and points of inflection and sketch the graph ...

Q: You are given the four points in the plane A=(8,−8), B=(10,4), C=(12,−1), and D=(16,1). The graph of...

A: We have given the four point in the plane A, B, C and D.The total integral is to be the sum of the a...

Q: During the first four months of employment, the monthly sales S (in thousands of dollars) for a new ...

A: Part (a)S= S(x)= 9 / x + 10 + x / 4, x ≥ 4The given function is defined only for x ≥ 4. We don't hav...

Q: How does the limiting behavior of solutions depend on the value of y(0)?

A: Given autonomus differential equation:Graph of function f is given.We need to show the the limiting ...

Q: Find the area of the region described. -4x and xIn 3 The region bounded by y e. ye X The area of the...

A: We first draw a rough sketch of y=e^x, y=e^-4x and x=ln 3And find the region bounded by them.

Q: Evaluate the integral in cylindrical coordinates. Please see attached image.

A: To calculate the value of the integral in cylindrical coordinates which is shown below,

Q: Find an equation of the tangent line to the curve at the given point. y x-2x + 1, (2, 5) Need Help? ...

A: We know that the value of slope of tangent to the curve y=f(x) at (a,b) is the value of dy/dx at (a...

Q: What is the particular solution for y′=5ex −6x3 +4x such that y(0)=−8? Do not include "y=" in your a...

A: The given differential equation is, y′=5ex −6x3 +4x.

Q: Find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)=−2x2+2x+3.

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Q: Logarithmic differentiation see below

A: The given function is ,

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Q: find the exact length of the curve of the equation in the picture below make sure to show all work

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Q: Find the derivative of y with respect to x

A: we are given an inverse function

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R i...

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A: Given:The integral is

Q: y = t(lnt)2 Find the derivative

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Q: If fx)x3x+1 then fx) (In x]3x (3x+1}x3x (2x+ In xr3x+ 1 3x13r 3 Inx 3x+13 In x

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Q: How can I get the result? Which is the result?

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Q: Find the domain: g(x) = ln(e^x -5)

A: The domain of ln z is z>0. We'll use the same concept here. So e^x-5>0.

Q: 8xy′+4(ln x)y)(4) +5x3 y′=−6x4 y−9xy″ What is the order of the differential equation shown above?

A: The given differential equation is, 8xy′ +4(lnx)y4 +5x3y′ = -6x4y - 9xy″.The order of the highest d...

Q: Find a formula for the general term an (not the partial sum) of the infinite series (starting with a...

A: Given infinite series is,

Q: Find the volume of the solid generated by revolving the region bounded by the given line and curve a...

A: The given curve is,

Q: Only problem I'm stuck on for this assignment please help!

A: Hi there! The question is having many sub-parts. Since no specification is given, only first three s...

Q: 1) If an odd function h(x) has a local maximum value at x c, can anything be said about h at the val...

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

Q: Suppose that a particle has been shot into the air in such a way that the rate at which its height i...

A: v = 320 - 32tIf h represents the height of the particle at any time t, then:v = dh / dt = 320 - 2t

Q: please explain how to solve this

A: (a)We are given graphand we can locate upper and lower curves on different regions

Q: Use the substitution formula Integral from a to b f left parenthesis g left parenthesis x right pare...

A: Obtain the value of the integral as follows.

Q: A train is initially traveling at a rate of 5 miles per hour. The acceleration of the train is 5 mil...

A: Given: The acceleration of the train is 5 miles per hour squared. That is, a(t) = 5.The initial velo...

Q: a. Find all points on the graph of f at which the tangent line is horizontal. b. Find all points on ...

A: We first find the slope of f(x) using differentiation.

Q: Hello, How is tan^-1 (tan (6pi/7)=-pi/7 possible? I don't know how it should be a negative or to use...

A: First consider:

Q: Find the average value of the function f(x) = e-4x on the interval [0, 1/2 ]

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Q: how to find Find the area of the region enclosed by one loop of the curve. r = sin(4θ)

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Q: Help on #2

A: To find the arc length of r(t)=i+tj+2tk in the interval [1,2]

Q: 15. A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 feet above ...

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Q: Find the values of the convergent series [from k=4 to infinity] E (2/3)3n-1 (-4/7)2n+3 *that E just ...

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Q: The rectangular coordinates of a point are given. Find polar coordinates of the point. Express 0 in ...

A: Let the polar coordinates of given point are ( rcos(thita), rsin(thita)) as shown on board.By compar...

Q: Find the work required to move the object on the line segment. Please refer to attached image.

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Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...

A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...