5. What is the coefficient of x''y" in the expansion (- 3x + 4y)ª . Show your work here:

Q: 14. Evaluate the integral: | ze dz. 1

A: Integrating by parts.

Q: 1. Evaluate the following integral: la 2x³ 2x5-x-4x³ + 1 (a) analytically, (b) single application of…

A: NOTE: As per the guidelines we are supposed to answer only 3 subparts question. Please upload it…

Q: 1+e-* Show that dr diverges.

A:

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given, x1/2+y1/28 where n=8 total number of terms =8+1=9 middle term =n2+1 82+1=5 5th term is a…

Q: Evaluate the integral of ax^2 e^-bx dx

A: We will use the "integration by parts" method to find the evaluation of the integral.

Q: (2x2 + 3)3 1. (5x3 + 5)3

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the remaining…

Q: 5. Find the indefinite integral 6.x²dx (2x³ + 7)3/2

A: The solution for the above question is as shown below.

Q: 1) Find the dexivative by the limit process. fex> 2X - 3 3X +4

A:

Q: -25 Evaluate the integral: dax x²Vx2 +25

A:

Q: Find indefinite integral e2x - p- e2x +1

A:

Q: evaluate the indefinite integral.

A:

Q: Find the constant term in the expansion

A: We have to solve the problem

Q: 7 Evaluate the improper integral, if exists : dz (5 - 2)3

A:

Q: The series 2" (n!)2 n=1 is divergent. Select one: True False

A: The given series is a 2n/(n!) 2. Repost the next question.

Q: 2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

A:

Q: Find the domain at the Furetion Iこ1パー25 rate in intervul Notation x4

A: Given f(x)=x2-25x4we have to find the domain of the given function

Q: Evaluate the integral. 2 sinh (4x- In 8) dx 2 cosh (4x - In 8) +C (B) cosh (4x - In 8) +C C) * cosh…

A:

Q: 2. (a) Show that when x > 1, In(x) (This should be very short.) (b) Use your knowledge of integrals…

A: We have to show below given expression

Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

A:

Q: Given the integral of- 2x with respect to x. x2+x-12

A: Please refer to the image below.

Q: From the Fourier expansion of f(x) = la- x) (x(1+x) -1<x<0 V. show that

A: Solution

Q: 1. Evaluate the integral

A:

Q: Use Heaviside expansion theorem (4s^2+7s+1)/s(s+1)^2

A:

Q: 10. Find the integral of dx x²-4 O In() + C x-2 O In() + C 2x x+2 O fIn( *2) + C X+2 O In() + C x+2…

A: *using concept:- 1. Partial fraction. 2. int(dx/x) = ln(x). 3. ln(m) - ln(n) = ln(m/n).

Q: (i) Find the constant term in the expansion of x+-

A: You have given 3 different questions in picture, without mentioning any particular questions. We can…

Q: 1 1. Evaluate the improper integral or show that it is divergent. (3x +1)

A:

Q: 2. (a) Use the definition of the derivative and the Binomial Theorem to = nx"-1 for any x" is f'(x)…

A: Since you have asked multiple question, we can solve first question for you. If you want other…

Q: The interval [0, 4] is partitioned into n equal subintervals, and a number x, is arbitrarily chosen…

A:

Q: Determine maximum error between 0.9 ≤ ? ≤ 1.1 interval for second degree Taylor expansion of ?(?) =…

A: find error

Q: 5. Evaluate the integral " Vtan o dex 1. de in terms of beta and Vtan gamma functions.

A:

Q: | 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1…

A:

Q: 2/Solve the following sequence X(n)= n. "u(-n) by using the differentiation property of the…

A: As per the question we are given the following sequence : X(n) = n (1/9)-n u(-n) And we have to find…

Q: suppose the quantity of a substance, Q, decreases by 6.5% in 10 hours 1. find a formula for the…

A: The decay model is represented by,

Q: 23+dt (4+3 Co+ 3+)5

A:

Q: The integral x²/4 - x²dx can be determined using the substitution 4- x2 = t.

A: Given integral: ∫02x24-x2dx

Q: 1. √2x+1 -15 2. So √x+1dx -0.5 3. 5x(1-2 4. fx√x-3 5. fx √x+1

A: The given integral is  ∫015xx+1dx

Q: Find Residues by using Lourent's Series f(²)=3/²2 at Z₂ = FL

A: Given f(z) = zz2 - 1

Q: Evaluate the following limit using Taylor series. 1.3 7 tan (x) - 7x +* lim 5 2x 7 tan " (x) - 7x +x…

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Q: In 8x Evaluate the definite integral : S dx 5x4

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Q: 6. Evaluate the fallowing real integrals by residue theerem 3 do ans금 t cosG+ 2sing +3

A:

Q: Evaluate the indefinite integral. (Hint: Expand the binomial.) 8. dx 3= 3 +

A:

Q: You found that the reduction formula of a certain integral is In = 180 (13x" sin (13x) + næ"-1 cos…

A:

Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

A:

Q: 8. The improper integral | 1. x²+2x+5 1.

A:

Q: Determine the one dimensional DFT for the following sequence x(n)= { 0,\ / 7 / l }

A: Sol:- Given Sequence :- xn=0,1,7,1One Dimension DFT  is given by Xw=11111-j-1j1-11-11j-1-j0171

Q: Evaluate the following limit using Taylor series. 12x - 72x° - 2 sin 6x lim 4x° 5 x-0 12x - 72x° - 2…

A: To find: Limit by tailor theorem

Q: 4x Evaluate the indefinite integral. 1ª + 1 IP-

A: The given integral is: ∫4xx4+1dx

Q: 23: Evaluate the integral of ſ (5y+7) 5 dy

A:

Q: Use (3) from Section 5.4 to evaluate the integral. In 6 e* dx =

A: