Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. d.x +C Væe(20V)

Q: 3x -dx be given. If 4=e*+2. then the resulting integral is f(u) du.compute f (3). e* +2 Let 2 (A 3 B...

A: We have to find value of f(3)

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A: The given series is ∑k=0∞78k+2. We have to check whether the series converges. To check converges we...

Q: Show that the lines having the equations 4x – 3y + 12 = 0 and 8x – 6y + 15 = 0 are parallel. |

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Q: x In(2 + x³) dx

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Q: Assume that g(x) is a function given by 2.x? + 3x +2 g(x) = x² + 2 Prove that g(x) is bounded for al...

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Q: 5x? tan( 3x³) dx. fu= 3x³, then the resulting integral is f(u) du. Find A Given: 4 A none of the cho...

A: Topic:- application of integration

Q: Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduc...

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Q: uestion 9 x2 dx. Which of the following options is correct? 00 onsider 9+x6 (A Arctan 3 + lim Arctan...

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Q: Inz Let U = ry ,x= Vst, y = s? - 1². Use the chain rule to find when s = 1, as 4. -. t = 2.

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Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² = 1...

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Q: Use the binomial series to find the Maclaurin series for the function. 4 f(x) = V1 + x 1 f(x) = 1 +-...

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Q: Using u-substitution, the integral f(x)dx Srwax u+1 reduces to a new integralg(u) du. If g(u) = , ev...

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Q: topic: calculus of polar curves 1. Find the slope of the curve r = 2cos 4Ɵ 2. Find the slope of th...

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Q: a) The function m-x+e*,x=0 f(x)=- 2n, x>0 is x' -16x x<0 x - 4x continuous for all real values of x....

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Q: d?y Find dr2 for the functlon: .3 3x +4x y=x

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 4 %3D P4(x)...

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Q: Question 10 cot (2x) Evaluate the integral Vcot (2x)- 15 cse (2x) A) --Arcsec 4 4 cot (2x) B) Arcsec...

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Q: Solve the following ODE. y" + 2y" – y- 2y = 9 - 123 NOTE: Write arbitrary constants as c1, Cg, and c...

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Q: Given a period function f (x) with a period p = 4, -2 < x <-1 f(x) (0, -1 < x < +1 %3D +1<x < +2 (a)...

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Q: Use the difference a41 - a, to show that the given sequence (a,] is strictly increasing or strictly ...

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Q: 2) An agriculturist wanted to plant seven different organic crops in a small field. To properly stud...

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Q: 2. (a) Prove the following inequality n(n- 1) ,2, 120 (1+ 1)" 2 1+ nz + 2 for any n 2 1. (b) Show th...

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Q: Evaluate the integral 4x4- 12x2 +7 xdx.

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Q: Determine the equation (both standard and general) of the following conic sections based on the cond...

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other...

Q: Questão 2 Check thatF(x, y) = (ez+y – y2 – cos(y))i + (ez+y – 2yx + xsen(y))j is a conservative fiel...

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Q: Use the limit comparison test to determine whether the series converges 8. 74 +5 The series Save for...

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Q: Market research for a certain ice cream company indicates that if the price per cup of ice cream is ...

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the ot...

Q: dy 2. V16 + y²

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Q: Use the Squeeze Theorem to evaluate lim sin(tan r) sech(secr). ес

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)*+1k! (2k ...

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Q: The graph shown is f(x) = sin x. What is the integral that defines the area under this line between ...

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Q: Question 7 If the solution to Je2x sec²(e2x*1)dx is equal to ktan (e2x+1) + C, find the exact value ...

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Q: O g(x) = (3t+ 2) dl t %3D

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Q: The graph shown is f(x) = 2x2 - 2. What is the integral that defines the area under this line betwee...

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Q: The following diagram shows a sketch of a curve with equation y = f(x). The points A(-3, 0), B(0, 0)...

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Q: Determine whether the given series is absolutely convergent, conditionally convergent or divergent. ...

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Q: 12x +1 S dx. (2x - 1)2 (3x + 2)2 Evaluate: (2x – 1)3 (3x +2)3 A) + C 3 8 in |(2x- 1)2 (3x+2)2| + C 1...

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Q: II. Determine the derivative of the ff. logarithmic functions 4. y = 8 log , 7x² 5. y = - 5 log , (1...

A: As per our guideline we solve only first three parts

Q: Consider the following sequence: 5" {an} = n=1 An+1 Use the ratio to show that the given sequence {a...

A: Given sequence an=5n2n2n=1+∞

Q: Use sigma notation to write the Taylor series about z = 1, for the function. 3 In z; z0 = 1 k =

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Q: Determine whether the given series converges or diverge E3n°4-n n=1

A: solution:-∑n=1∞3n34-n an=3n34-n an+1=3n+134-n+1 Ratio testL=limn→∞an+1an=limn→∞3n+134-n+1 3n34-n =li...

Q: Find the radius of convergence and the interval of convergence. Σ k(k+ 1) k=1 1) First apply the Rat...

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Q: Graph the two equations x+y= 0, and y = - (x-1) and find the points in which the graphs intersect

A: 1. Given x+y=0y=-xtf x=0,y=0if x=1 ,y=-1if x=2,y=-2Graph passing through origin .2. y=-x-12if x=0,y=...

Q: X+ tan (xy)=0

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Q: Question 14 3r dx be given. If u=e+2, then the resulting integral is ex+2 du. Compute f (3). Let A n...

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Q: dx (x² + 9)² 5.

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Q: u+1 Using u-substitution, the integral Jf(x)dx reduces to a new integral glu) du. If glu) = , evalua...

A: Given  g(u) = u+1u and  ∫f(x) dx = x + lnx-1 + C

Q: 8 プ+5

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Q: Followings are given for f(x) function and its derivative f' (x) Sf(0) =1 f' (0) =5 |F(2)=3 f' (2) =...

A: The given problem is solved below in detail.

Q: 1. Let (r + 2)², if I 0. (a) Give the r coordinate(s) of the possible point(s) of discontinuity of ...

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