Find the length of the curve. 1) y = (16-x2/3) 3/2 from x = 1 to x = 64

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A: According to question,Given Series,∑n=1∞ 89n2+3n-2

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A: Since you have asked multiple questions, As per the guidelines we have to solve the first question.…

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A: An integral will be convergent if the value of integration is finite.

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Q: -5 -4 -3 -2 1 1 2 3 4 56 1 interval(s) on which f is increasing. (Enter your answer using interval…

A: We  will find the required.

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A: Two concepts Trigonometry equations Logrithmic rule

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Q: So 1 er+e0.5a ex dx

A: Given query is to find the integral.

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A: Given: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing…

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A: Water is being pumped into an inverted conical tank at a rate of 6.9 cubic meters per minute. The…

Q: S₁ 9 $₂ = 81 X $3 $4 55 9 Σ; 27-1 n = 1 = X

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Q: 11. Find the maximum and minimum values of the function f(x, y) = 3x + y - 4 on the curve ² + 2y² =…

A: To find the maximum and minimum values of the function. fx, y=3x+y-4 on the curve x2+2y2=38.

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Q: Suppose y = √2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy X…

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A: To solve the following problem.

Q: Use the Laplace transform to solve the given integral equation. + 6 ² ₁² - f(t) + f(t) = cos(t) (t =…

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Q: 4 2 Find all of the critical points of 2 = =+ = -xy. Identify each point as a Y local minimum,…

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A: If function f is decreasing then f’(x) <0. Use this concept.

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A: Given query is to find cosK.

Q: Please help (41-45)

A: Here we have to find the derivative.

Q: -Calculate the minimum for the function f(x, y) = 2x² + 2x^² - xy

A: According to question,Given Function,fx,y = 2x4 + 2y4-xy

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Q: (a) 3 inches is what part of a foot? (b) 3 inches is what part of a yard? (c) 2 dimes is what part…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: show that: 3 [ f(x) +1] = gf(x)=x²-1, x +4+3 f(x) = f(x) - X-1

A: Given that : f(x) = x2 - 1 and we show that: 3[f(x) +1] = x + 4 + 4f(x) - f(x)/(x-1).       Here i…

Q: 7. Let E be the ball of radius 1 centered at the point (0, 0, -1). (a) Show that E is given in…

A: The solution is shown below-

Q: Find the volume under the graph of the function f(x, y) = 4x³y over the region shown in the figure…

A: Consider the function and the region  f(x,y)=4x2y

Q: 4. Find the solution to the initial value problem y'= 5(2-y), y(0)=5. Report solutions in y equals…

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Q: (a) 2n - 31 4n + 1)₂ { ∞ n=3

A: Solution: Given data, (a) { (2n-3)/(4n+1)}ₙ=3∞

Q: Find the general solution of the given differential equation. y'' + 18y' + 81y = t−2e−9t,   t > 0

A: Given

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Q: Solve the initial value problem below using the method of Laplace transforms y" +9y=45t² - 54t+ 64,…

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Q: Show that the following vector fields F are conservatives and find ALL f such that F = Vf. (a) (b)…

A: As per guidelines, we can solve only first question if multiple questions are posted, please repost…

Q: 13. Find all the critical points of the function f(x, y) = xy + x+y xy and determine if they are…

A: To solve the following problem and find the relative extrema

Q: Use the chain rule to find and , where First the pieces: 器 Әх Əs ду Əs || dt - || || And putting it…

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Q: According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not…

A: note: as per guidelines we support only three subparts of the question . kindly repost next question…

Q: 9. (a) A region is bounded by two lines and a quadratic polynomial with the following conditions: .…

A: image is not properly clear

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: The solution is shown below-