Find the arc length (s) of the curve r(t) = (3t, 2 sin(2t), 2 cos (2t)) for -4 < t 5 S = Check Answer 244 116,535 AUG 15 tv

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A: Disclaimer: since you have asked multiple question , we will solve only first for you. if you wants…

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A: Formula for Integration by parts: ∫fg'=fg-∫f'g

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A: Question is solved.

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Q: (a) Consider the power series Show that B(x) converges for all x. B(x) = Σ n=0 (-1)η 2η 22n (n!) ²

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Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: The function f is shown below. What is the value of answer in simplest form. -10-9-8 -7 -6 -5 -4 -3…

A: This question is related to definite integration, we will solve it using given information.

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Q: In this question, consider the vectors 10 8 V1 ~- - ( ) - ~- - ( ) - - - () ---- () v2 = V3 = b and…

A: The objective of the question is determine the coefficient matrix" A" without simplifying.

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Q: Find the area of one leaf of the "four-petaled rose" r = 7 sin (20). X FIGURE Four-petaled rose (Use…

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A: Here we can express f in standard form in the following steps.

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A: Let's find tangential and normal components of acceleration.

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Q: Solve the differential equation dy dx y+√√x² + y² X ; when x x = a. y² = 2x-1 b. x² = 2y-1 2 c.…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: = Approximate the area under the curve y with 4 subdivisions. x³ from x = 2 to 4 using a Right…

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Q: Find f such that f'(x) = 9 √√x f(1) = 32.

A: Topic:- application of integration

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A: Topic- application of derivatives

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Q: Q3. Find the distance between the points AB and BC where A is (2,1,0), B is (-1,3,1) and C is (-1,…

A: The points A2,1,0, B-1,3,1 and C-1,0,1 we have to find the distance between the points AB and BC…

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A: Given.

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Q: Solve the differential equation xdy]=0 xdx +sin? (%) [yde 4x ln || - 2y + x sin ( ² ) = 0 2x a. 2y…

A: Given :   xdx+sin2yxydx-xdy=0

Q: Write the following expression as one integral. 3 5 3 [ -6 f(x) dx + f(x) dx - f(x) dx 0 0 3 5 3 $…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Here is the solution:

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given figure  with areas Now V=∫010f(x)dxV=∫03f(x)dx+∫35f(x)dx+∫57f(x)dx+∫710f(x)dx

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A: Let's solve integration.

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Q: Let f be a continuous function such that 2 Lª¸ ƒ(2) dx = - f(x) dx = -8. What is the value of -3 2…

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