Question 18 Find the length of the curve with the given vector equation. r(t) = (6 + 2t 3) i + (2t 3- 5)j + (4 - t3) k, 1 sts3 O 252 O 84 O 78 O 234

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Q: 3.) ž sin'(x)dx

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A: The given integral is Sin(3x)/[1+cos2(3x)].

Q: Find the indicated limit or state that it does not exist. x2y + xy2 lim (x, y)-(0, 0) x2 + y2 O 2 O…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise p…

A: As we know that; The Green's theorem; ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA   Given: I=∫C3xy dx+6xy dy And C:…

Q: -2 12) Find the sum of the Series 2".30" A C) D) 2 E) 9

A: Let    I= ∑n=1∞2n3-n-2Rewriting 2n3-n-2=2n3-n3-2                                  =2n3n×132…

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A: Volume

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A: As per our guidelines, we are supposed to answer only one question. Kindly repost other questions as…

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Q: Determine whether the given improper integrals are convergent or divergent. Evaluate those that are…

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Q: Find the radius of convergence, R, of the series. xn + 1 3n! n = 2 R = Find the interval, I, of…

A: A detailed solution is given below.

Q: INTRODUCTION TO MATRICES Answer the following questions: Given the Matrix A below. 3 12 21 A- 17 15…

A: This is a problem related to matrix . Based on the general formula and concepts we will answer the…

Q: Evaluate the iterated integral. 7 8 6 | // * +v° + 2²) dx dy dz -6 0 0 / /(x² + x² + z²)dx dy dz i…

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Q: 5 6 2 16 41 If =2 4 1 and B-3 3. find the sum of AB. 3 3 2

A: Matrix ab

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Q: Determine the vector field of F. F(x, y) = yl – x) 1.

A: Vector field

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Q: Give the representation, equations and solution. Use elimination, comparison or substitution to…

A: A detailed solution is given below.

Q: Question 22 Solve the problem. Calculate the area of the parallelogram with v = (-6, 0, -6) and w=…

A: solution

Q: r3 5x-2 5.) . V5x+1 xp!

A: This is a problem of integration. Based on the general formula and concept we will answer the…

Q: =/2 4. cos z dr Jo da 5. I+1 I +IA

A: We have to evaluate the indefinite integral

Q: (2))? dz: Consider the indefinite integral a) This can be transformed into a basic integral by…

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Q: Find curl(Sz i+6x j + 7y k), curl(Sz i+ 6x j + 7y k) =( i+(

A: This question van be solved using the concept of curl F.

Q: Question 20 Evaluate the integral. TT/4 (8 cos ti +9 sin tj) dt -TT/4 O 9N2 i O &2 i+92 j O &V i

A: Topic = Integration

Q: x")' = a xa-,(x)'=1 and (constant )'= 0. %3D x+2 Using Quotient Rule (£)' = f'g-fg') x-1 A) 2x/…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. (y - x) dx +…

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Q: Find curl (5z i + 6x j + 8y k). curl (5z i+ 6x j + 8y k) )i + ( i )j + ( i i )k

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Q: I would super appreciate some direction with this problem.  Would I need to change this to polar…

A: Explanation of the answer is as follows

Q: 4x d.x J V3 - 4x – 4x2

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Q: 13) which of the following Series convenge' 7n Ci) In hzg

A: i)∑n=1∞ 17nThe series diverges by p-series test.(∑n=1∞ 1np converges only when p&gt;1)=17∑n=1∞…

Q: ||r(t) × r" (t)|| ||r(t)|* Use the formula k(t) to find k(t). 3 r(t) = 7 cos(4t)i+ 7 sin(4t)j+ 5tk…

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Q: (b) The curve y = x +3x, from x 1 to x = 3 (c) The ,2 1 from 2 to g

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Q: ててーXつ (ーフ 1 प. ८ genc 16)Find the power Series S こひ( れこス て24(O t2u(コ

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Q: Find the area bounded by the curve y = 9 - x2 and the x-axis. a) Horizontal Strip b) Vertical Strip

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: B)号 4. nこt u puyと いつ0o Sinlen)+ w!l いo an

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Q: Find V (V x F), if F(z, y, =) = 3e""i+7ze'j – 3e"k. V. (V x F) =

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Q: he Taylor series for fx) centered at the given Val f(x) = x- 6x2 + 2, a = 2 %3D E"e(x- 2)" = -6 +…

A: Taylor series

Q: True or False. Explain your answer The limit of sin(x) as x approaches very large values is 0 or 1.

A: Given

Q: Question 1 Find the centroid of the given region. y-2- A (8/23,76/111) B (5,15) (c (3/22,45/61)…

A: The expression for the centroid is: For the x coordinate of the centroid: x=1A∬xdydx  For the y…

Q: Evaluate F• dr. F(x, у) — хі + уј = xi + yj C: r(t) = (7t + 9)i + tj, 0stsi

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Q: Solve the following differential equations of 2y – -3d = y* . e" ;

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Q: n² < 2" for n = 4, 5, 6, ... (Hint: 2n + 1 < 2" for n= 3,4,5, ...)

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Q: Question 5 Find the volume of the solid that results when the region enclosed by the given curves is…

A: Given, y= sqrt(25-x²) y= 4

Q: Evaluate (2x - y) dx + (x + 5y) dy.

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Q: 1. If = (1.0.-3) and i = (6,-3,-4) compute ixw.

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Q: dz 14. Evaluate S z(4+2)

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Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

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Q: Question 2 of 4 (x² – 1)(x + 1) (x2 – 2x + 1) :- f (x) =

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