| 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: (15) If X-exp(1), then (a) 2X-exp(2) (c) 2x~exp (¹) O a O b O C Od (b) 2X-X² (2) (d) 2X-G(2,1) is

A: Given that X~exp(1) then  We have to find 2X follows which distribution:

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

A:

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

A:

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

A:

Q: 3. Nadia's Fashions d ing a new sales pro (a) Find N'(4).

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

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: (213)(4*) Simplify (8+3) O t3 2 O 2t3 O 1

A: Solution:-

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

A:

Q: en-3h-S If y= show that day (on-3)* 2n-3

A: Given function is  y=ex^2-3x-52x-3                           ⋯1 To show:…

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: x² – 4 Evaluate: A =Vx2-4+ sec-스)+C ⑥ -Vx2-4+2 sec-스)+C =V x2 – 4 – 2 sec + C (D =2Vx2-4+ sec-1스)+C…

A:

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: 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: N1/2 (x) = -J_1/2(x) الخيار 4 J1/2(x) الخيار 3 J-1/2(x)

A: The equation that describes the relation between the Bessel's function: Jvx and the Neumann's…

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

A:

Q: Evaluate L{cos² 3t} s² – 18 a) s(s² + 36) s2 – 18 b) s(s² – 36) s² + 18 c) s(s² + 36) s2 + 18 d)…

A:

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

A:

Q: 4(-1)" Σ 3) Estimate 2N 1 correct to one decimal place. N-1

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

A:

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.…

A:

Q: V = So 29 (3+2)(1-√5) dys

A:

Q: Evaluate х3 (x* — 1)3 dx x*(x* – 1)ª + C (x* – 1)* + C 16 4x4 (x* – 1)4 (x4 – 1)4 + C 16 + C 4

A: The given integral is; Integration of x3(x4-1)3.

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)