Use the Alternating Series Test to show that the series is convergent. +oo (-1)"+1 Σ 3n n=1 Answer it by using (i) and (ii): (1) an+1 < an (ii) n→十00 lim an 0,

Q: Evaluate the integral tan 4x S- Vtan? 4x - 24 O 1 Arcsec sec 4x + C 5 sec 4x + C 5 O 1 Arcsec 20 1 A...

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Q: Write an equation of the tangent line to the graph of f(x) 3x at x = +1. %3D 1+2x2 For what value(s)...

A: Given that fx=3x21+2x2 Solution :fx=3x21+2x2f'x=6x1+2x2-4x3x21+2x22if f'x=06x1+2x2-4x3x21+2x22=06x1+...

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Q: 21. du Form Answer u 5sinx Ex. S V3+ 2cosx 3+ 2cosx -5V3 + 2cosx + C dx -2sinxdx Given: J – 3x 3 dx ...

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Q: 8. dx du The integral reduces to k, where u = f(x) and for some ex + 1 constant k . Compute f(1). e ...

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Q: 5. у %3D 88 8x + 888 6. у %3D 2021 7х'6 7. у %3D 5x3 е 4x -5 8. у %3D 20 е -4x x2 - 10

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Q: 4x3 %3D 1. mtegrate. de - aya dx 4x3 du = 4x° dx %3D Jxt -2 xp: こ -112 du te 2(x*- 2) ° +C %3D %3D

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Q: ue Theorem on the given interval? ction satisfies the Mean Value Theorem. continuous on [0, 3] and d...

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Q: Given the matrix below, determine the following:  a. Cofactor of the element 5 b. Cofactor of eleme...

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Q: 00 k k 2. Σ (- 1)- k+1 k=0

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Q: 3. Verify that each of the following statements is a false statement by finding a counterexample for...

A: Both statements are false : We can verify by giving an example. In the first statement for x=2 , sta...

Q: Evaluate the iterated integral by converting to polar coordinates. V2x – x2 5/x2 + y² dy dx

A: Explained below 

Q: Given: 5e-x-6e-3x Find: u O 5e-x - 6e-3x 5e2x – 6 5-бе-2х V5e-x - 6e-3x

A: ∫ex5e-x-6e-3x3dxSubstitute v=ex→dvdx=ex→dx=e-xdve-3x=1v3e-x=1v=∫15v-6v33dv

Q: d*y 4. Find 5 of the function f (x) = - e dz"

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Q: V9 – x2 Let R be the region bounded by the curves Consider the function f(x) = 3 y = f(x) and y = 0 ...

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Q: Given: S 2x (3-5x+)'dx Find: Formula O -2 Ju'du 0 2 fu'du o fưdu Jư du 10

A: Given problem:-

Q: 14. If we let u = 4x – 1 for the s²tan(4x-1)-3 cos"(4x-1) dx. what will be the cos(4x-1) resulting f...

A: This is a integration problem

Q: Sar en x² dx Given: Find: Formula o fe"du Sa"au

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Q: Use the Intermediate Value Theorem to show that 2х - 3 if – 3 0 has a zero on the interval [-2, In ...

A: By using the Intermediate Value Theorem to show that fx=2x-3x+3  if -3&lt;x≤0-3+2 cosh x  if x&gt;0h...

Q: . Set up the integral with represents the area of the surface z = xy that lies inside of %3D the ell...

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Q: dx Evaluate 2 xV x2 - 4 4 O O

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Q: dx x² Vx²-1 -2.

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Q: dx 2V x3 - 3x x

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Q: 3. y = x³ – 3x² + 2x – 6 ACTIVITY 1. Find the deriva 1. f(x) = -2 2. g(x) = 4x3 %3D 2 %3D -

A: Solution:As per our guidelines we are supposed to answer only three questions. Here  f(x)=-2

Q: 18. dx The integral - can be rewritten as V1 - x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī -s) s--00 s--00...

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Q: Given F(s) = L(f), f(t), a, b, L, n are constants. Show the solution. 1 1) (s+v2)(s-V3)

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Q: One of the following is an improper integral. - In 3 e* dx 4 – ex dx In 2 xV16 – In x dx cln 2 dx x ...

A: In this question we have to find the value of Improper Integral. Note: As per our policy we are supp...

Q: 2. (а, By completing the square, show that 1/2 d.x x2 – x +1 3/3 By factoring x³+1 as a sum of cubes...

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Q: Evaluate the integral tan 4x dx tan? 4x 24 O 1 sec 4x Arcsec + C - Vtan? 4x – 24| +C n tan 4x + 1 -A...

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Q: 5. Solve a) In(x+1) = 3 b) e2 – e = 2.

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Q: SV5+12x? - 4x4 xdx 2x2 - 3 (2x2 - 3)/5+ 12x? – 4xª + 14Arcsin V14 +C O (2x2 - 3)/5+ 12x² – 4xª + 14I...

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Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: 6. Which of the following is not true about function? a. Function is composed of two quantities wher...

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Q: 1 |dz 4z

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Q: The graph of a function f is shown below. 2 -4 4 -2 -4 For the following questions, note that you ca...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: dz 4z+z' ,2

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Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A: In the taylor's expansion when a=0 , then it is called maclarian expansion.    

Q: Example Find the domain and range of the following functions : x +7 if - 35x<5 [2-x if 0 <x<2 x - 1 ...

A: (i) f(x)=2-xif 0&lt;x&lt;2x-1if  3≤x&lt;4(ii) f(x)=x+7 if  -3≤x&lt;5x2if   5≤x&lt;76-2xif   x≥7

Q: 6. Find f(x) so that when w fG) the integral 1+ Inx dx can be tan(f) cot u du. rewritten as (a) x+ 1...

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Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:  

Q: S2x3 (3- 5x4)"dx Given:

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Q: (x – 2)2 sin(2x2 – 3x – 2) lim log1 r+2+ 3

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Q: 1 x + 3

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Q: 2. If we visualize the region having "right" and "left" boundaries, express each as functions of y a...

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Q: Find the equation of circle and the equation of line from the following graph (3. -4)

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Q: the trough is being filled with water at a rate of 0.2m3/min0.2m3/min

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Q: HON 3 tan(e-*) dx Given: ex Find: du O e-*dx O -e-Xdx exdx O - e*dx

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Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for ...

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Q: 4. If u = f(x), then k +C for some constant k. dx = x* + 2x2 + 1 x² + 1 Compute kf (1). (a) 4 (b) – ...

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