| grk(1 – 2)n=k/(") z*(1 – 2)n-k | 2*(1 – : 1/2 1 2n/2 how did we get step 3 from step 2 ? explain in details. VI

Q: True or false: The coefficient of x4y7 in (3x – 4y)11 is (2)347. True False

A:

Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: 36x12. -1. Provide appropriate 6x6 –1 (b) Find the least integer n such that f(x) is O(x") for ƒ(x)…

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Q: 1 (x² - y²)² x+y valuate: ²₁₁² dx dy

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Q: JUX² +2x-8 dx Evaluate lx + 1Wx + 1)* + 9 = l(x + 1) + Vtx + 1}² – 9|]+c 9ln (+ 1)/(x + 1)² – 9 –…

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Q: If g(t) = £? (e-35-*), a farmula for L (e* g14) is? -8t +8 a) ede+25 b) e 3e+17

A: Given g(t)=ℒ-1e-3s-7

Q: Give a combinatorial proof of the identity (2)=3(") + ³(²) 3(3).

A: The combination formula is defined as (nr)=n!r!(n−r)! Therefore…

Q: 21 _) P') pludx= чи (и+1) сеn+ л 2 и+31 и+1

A:

Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: Show that if (B) (C) N N then the value of neither x nor y can exceed 1/4. (A) N = X, 2x, = 3x and…

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Q: a) 6e2x – 17(e*) + 12 = 0 b) 82x+1 = 45-x %3D

A:

Q: Find L[te®]

A: We can solve the problem using following properties: eat = 1(s-a)Multliplication by T t.f(t)  =…

Q: (- 1)"x" Σ 6" (n² + 9) n=1 8.

A: Given

Q: dthe She (5y-3)

A: We have to find (5y - 3)2

Q: how to show the following coefficient is less than 1

A: Given information: An expression involving gamma function is given.

Q: k-1 k-1 C1(k) = A + 1/½ 2* + 3½i²(/½)* i=0 i=0 A – 1/½(1 – 2*) – 6[(1/½k² + k + 3/½)(/2)* – 3/2] =…

A:

Q: Smplify (gizi) (i 131)(5+41)

A: First we will find the multiplication of two factors. Then multiple the result by rest factor. Here…

Q: 3. Find the sum of all values of k such that 2k k -dx =15. (A) 3 (B) 2 (C) 1 (D) 0 (E) 1/2

A: ∫12kx-kx2dx=15∫12kxdx-∫12kkx2dx=15∫12kxdx-k∫12kx-2dx=15x2212k-kx-2+1-2+112k=15x2212k-kx-1-112k=15x22…

Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: (15.2): Find In(x) – In(x² – 1) +2 In(z +3) 3

A: Find 13ln(x)-lnx2-1+2lnx+3. Logarithmic properties used: alogcb=logcba logca-logcb=logcab…

Q: has its largest value. a = Find two numbers a and b with a ≤ b such that b= # # L (6-52 (6-5x-x²)…

A: Given integral is ∫ab6−5x−x213dx. We have to find the value of a and b with a≤b. The integral…

Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: dx 11 J V64x2 - 121 8 11 18 – In-x+ 8 3 A +C 64x2 – 121 B In 1 V64x2 - 121 +C 11 In V64x2 - 121 +C…

A:

Q: (z- 1) The residue of f(2) = at z = -9 is -9e9 (z + 9) Select one: O True False

A:

Q: π Show x² x² + x² +1 4 √3 -∞0 4 Hint: x² + x² +1= (xª + 2x² +1) − x² = (x² +1)² −x² dx =

A: The objective is to show that ∫-∞∞ x2x4+x2+1dx=π3

Q: Question 5 (Show your work!) Find the coefficients of 2. r* in (r2 - (1/x))". |

A: (x²-(1/x))^n

Q: „¸ 1) and ♂ = (1, 1, 2). Find || ☎ – proj♂¯||. d) 2√3 3 (e) None of these

A:

Q: 2. What is the coefficient of x³y¹ in the expansion of (2x − y + 5)8?

A:

Q: n Prove that (3i – 2) = ; (3n – 1) for all integers n > 1. - i=1

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Q: z2+5z+6 "f(2) = and C: z=3, then f (z)dz =? %3D3• N-2 O a. 0 O b. #0 Oc f(z) is not analytic O d.…

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Q: V = So 29 (3+2)(1-√5) dys

A:

Q: Find In(x) – In(x² – 1) +2 In( +3) -

A: Our Aim is to find 13 ln (x) - ln (x2-1) +2 ln (x+3) -(i)