What is the integral of f cos¹ (2t)dt? Ot+sin(4t) + sin(8t)] + C None of the choices cos" (2x) sin(2x) 3 cos(2t) sin(2t) ++ C 8 16 sin(8t)+sin(4t)+24t 64 +C 25

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A: Solution of given question is written in below steps.

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A: The given geometric sequence: 32, 38,332,.....

Q: with

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Q: Integrate ze da Select one: O A. ex (2x-1) + C OB. e (x-2) + C O C. e* (x-1) + C O D. ex (x-3) + C

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Q: Question af If f(x, y) = xy² - x ln(y) find Ət if x(t, s) = s² - st³ and y(t, s) = e-st².

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Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = z =

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: Use an appropriate test to determine whether the series converges. Σ k=1 By the 9 k 12 9 this series

A: Please see the below picture for detailed solution.

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A: Solve the following

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Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

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Q: x(t) = £−1 x(t) = L−¹ S s² +5 3s² +9 4s ((s + 3) (s+5))

A: Last 2 question solved

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Q: Integrate 3+22 Select one: OA. 7Inlxl + OB. 4inlxl + O C. 31nlxl + O D. 5Inlxl + dz + C + C + C + C

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Q: Consider the function f(x)=5x2−9x7f Let F(x)F be the antiderivative of f(x)with F(1)=0 then f(x)

A: we have to find the function F(x) .

Q: -6 -5 -4 -3 -2 -1 5 of f(x) 4 3 2 1 -1 1 -2- -3- N 1 f(x) dx = 0 of f(x) dx > -5 Which of the…

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Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: To find the minimum distance from a point to a paraboloid is just to minimize the function…

Q: Use the graph of m(x) shown to answer the questions below. -5 10 50 0 5 a. State the domain of m(x)…

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Q: lim cot 1 -1 8418 1

A: A detailed solution is given below.

Q: Use an appropriate test to determine whether the series converges. k² +3 2 k + 3k +2 2k²+1 Σ k=1

A: The given series,        ∑k=1∞k2+3k+22k2+1

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Q: 3s + 12 망 (s + 2s + 10) x(t) = L-1

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Q: Evaluate cosh² x dx }(sinh2n +2) + 0 +x + C O2e²x +4z + C 8 O None of the choices cosh(z)sinh(2)++C

A: We can solve this as follows:

Q: In reference to the following function,  f (θ) = (θ − 3) cos(θ) Explain why the graph of f lies…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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Q: The volume of oil in an inverted conical basin is increasing at a rate of 3 cubic inches per second.…

A: The volume of oil in an inverted conical basin is increasing at a rate of 3 cubic inches per second.…

Q: Evaluate fz² In z dz using integration by parts O² Inz-+c Onz-+c Onz-+c 2²lnz - 2 + c 12 21

A: Solution:  step-1: Evaluate ∫z2*lnz dz using integration by parts                Formula for…

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Q: No 1 Problem Use the method of disks/rings to determine the volume of the solid obtained by rotating…

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