Confirm that the integral test is applicable and use it to determine whether the series converges. 1 (a) 3k + 2 k=1

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Q: Evaluate the following. 1. lim (2x – 11) x-4 x+4 2. lim x-2 l(x-1)(x+2),

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Q: Vx2 (b) / 4 dx; x > 2. x2

A: To find out the integration. 

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Q: function

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Q: 1. Consider the finite region R bounded by the curves x 2y? +1 and the curve x = y² +2. (a) Sketch a...

A: Find your answer below 

Q: Linear Approximation a) Find the linearization (L(x)) of f (x) = V1 + x at x = 3. b) Use L(3.2) to e...

A: L(x) = f(a)+f'(a)(x-a).

Q: 1. Use any appropriate method in finding the indicated solution of the following differential equati...

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple quest...

Q: 13. Evaluate the given integral by converting to polar coordinates ez²+y² R = {(x, y) : a² + y? < 3}...

A: Given

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Q: The Maclaurin series of the function f(z) = 3z'e-9 can be written as f(x) = Cn" n=0 where the first ...

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Q: 4. S (sint + cost t ) dt A - cos t + sin t + C C - cos t- sin t + C B cos t+ sin t + C D cos t- sin ...

A: 4. In this question, we need to find the integral.

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Q: Evaluate the Integral 6. J csc x sec x tan 2x dx ANSWER: T tan x+1 6. In + C tan x-1

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Q: At what point on the ellipsoid x2 + y2 + 8z? = 1 is the tangent plane parallel to the plane x + 2y +...

A: Given :   Ellipsoid : x2+y2+8z2=1 Plane : x+2y+z=1

Q: . Find a formula for the inverse of the function and show that fif'(x))=f'(fx)). 4х-1 a. y = V10-3x ...

A:  Note: - “Since you have posted a question with multiple sub-parts, we will solve the first three su...

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A: Given f(x) = x-3x2  to find local minimum values, find the values of x when f'(x) = 0

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Q: Evaluate the integral AP R = [0, 2] x [2, 4] × [-1, 1]. (y + z)2

A: As per the instruction, we will be solving only the first one.     ∫∫∫xy+z2dV=∫-11∫24∫02xy+z2dxdydz=...

Q: Solve the inequality involving absolute value. Please explain. |x- 2| + 6 ≥ 12

A: Given query is to find solution of the inequality.

Q: what is the directrix of this? (x-4)²=-24(y-2)

A: The given equation is  (x-4)2=-24(y-2)

Q: 7. e*-4e * dx A 2 C. + C 2 + C ex x + - - x +2 e * + C x - 2 e * +C C O E None

A: Here,               We have given an indefinite                             integral now we have to ...

Q: What is the area of the shaded region? y = sin x TT ST 6

A: From the given region; So, The point of intersection between the curve and line is: y=sinπ6=12y=sin...

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Q: 1 1 Зп — 1 3n + 2 n=1

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = x2 - 1 - In...

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Q: integration by substitution x(2x2+1)6dx

A: Substitute , 2x2 + 1 = t.

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Q: Approximate values of f(x, y) at sample points on a grid are given in the figure. Estimate , f(x, y)...

A: The given problem is solved below in detail.

Q: (-1)"n² n2 + 1

A: Topic: sequence and series  

Q: 2. Find the area of the region enclosed by y = 3.5x and z 9-y. %3D 2- 1- 1234 5 6 7 8 9 -1 of Use ho...

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Q: Find the distance between the points using the following methods. (3, 1),    (6, 9) (a) the Distanc...

A: Distance between two points (a,b)(c,d) is given by      L = d-b2+c-a2given points(3,1)(6,9)a.     L ...

Q: 6. 2x3+3x dx x4+3x2 C 1 In lx* + 3x21 + C + C In(x4+3x2) 1 1 In Ix + 3x21 + C +C 2 In(x4+3x2) A B O ...

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Q: 8. Find a definite integral for the area of the region that lies inside the polar curve r2 = 8cos(20...

A: Here, given that the region is bounded by the curves: r2=8cos(2θ) &amp; r=2 which is

Q: V lim x² – 9 X→3 x² – 4x + 3

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Q: Write the formula for the derivative of the function. f(x) = 11x4 + 15x3 + 9

A: Given query is to find the derivative of the function.

Q: 3. Find the arc length of the curve y =;x² --In x,

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Q: Find values of x, if any, at which fis not continuous. x – 1 + х2 — 1 3 f(x) = 1) Since the sum of t...

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Q: 12. Let R be the region of the plane R= {(r, y) : # 2 0 and ²+ y? < 2}. Describe R using polar coord...

A: Here, the given region is: R=(x,y):x≥0 &amp; x2+y2≤2

Q: A. Determine the indicated derivative for each of the following functions. x3 cos y 1. Find fxzy for...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

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Q: Which of the following series are alternating series? (Hint: It may be helpful to calculate the firs...

A: Let's find. 

Q: 19 4-x²

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Q: 2x5y ' = y(3x4+y2)

A: For the solution follow the next step.