6. Show that when 0 < |z – 1| < 2, Σ (z-1)(z-3) 00 --Σ n=0 = (z-1)" 2n+2 1 2(z - 1)*

Q: 4. Show that if ki = (X; – X)/[Σ(X; – Χ)2], then (a) Σ ki = 0; = (b) Σk? = 1/[Σ(X - X)]; (c) Σk;(X;…

A:

Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

A: We have given that.   X~N( μ , ?^2 )   μ=5 , ? =1   Z-score =( x - μ )/?

Q: limn→ 14+24+34+...+n n n5

A: Given problem:- limn→∞14+24+34+......+n4n5

Q: 5. In which annular domain is f(z) = (a) A(0,0,4) (b) A(0,0,2√2) (a) (b) 1 24 - 16 (d) holomorphic?…

A:

Q: Let f:(-1,1)→ R. f(x) = (2n)! 4" (n!) ² (2n+1) -x2n+1 and f(x) = f (x), xe (-1,1). Find f n=0 -…

A: Given Information:a) ;; .b) ; .To find:The value of  in both the sequence of functions.Concept…

Q: Let f(z) = 4r- 12x +7 then f(r) is decreasing on Select one: O a (-00, -1), [12, o0) Ob [1,0) O…

A:

Q: 13) If it is known that -6 L{e% f(t}} s2 – 14s + 40 with certainty it can be assured that: a) f(t) =…

A: We will first find F(s) the using inverse Laplace we will find f(t) We know…

Q: Let x 4 and y 2 yll₁=0 -0 ||x - y||₁ = ||x - y ||∞ = ||x − y||₂ = [3] 5. Compute

A:

Q: x+2y+3z=4 19. 3x+6y+z=2 (no solution) 2x+4y+z=-2 [x-2y+3z=4 20. 3x-y-z=2 x+y-3z=-2

A: Total Equations are 3x+2y+3z=4→(1)3x+6y+z=2→(2)2x+4y+z=-2→(3)Converting given equations into matrix…

Q: 2. (a) Let A = {x = [0, 1]: x has a decimal representation not containing the digit 5.} Show that A…

A: We shall use certain results from measure theory

Q: Find g" (1) for g (x) = xª – x³ + 2x -

A: Topic: differentiation

Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: 5. (a) Verify that t(n) = t(n+ 1) = t(n + 2) = t(n + 3) holds for n = 3655 and 4503. (b) When n =…

A: To find-  Verify that τn = τn+1 = τn+2 = τn+3 holds for n = 3655 and 4503 When n = 14, 206, and…

Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where x s player i's…

A:

Q: 3) You are given T(1 + 1x+3x²+(-4) x³) = =[ 2.70+ 1x + 2x²+(-3)x) - 2.7-1 + (-2)x+ (-4x+6)=[]) ‚T(0…

A: Note :- These are multiple questions and according to the Bartle by policy, we can do maximum 1…

Q: 1 Expand f(2) = -in the domain 4 < |2 < 12 (z-4)(z–12)

A:

Q: . Given P(x) =a( b – x) ( x+ c) ( dx+ 1) , where a, b,c and d are Re Z*. If the first term of the…

A: Given P(x)=a(b-x)(x+c)(dx+1) 1st term of expansion=-8x3 P(-3)=0

Q: 3. Give combinatorial proof of a k (") = n () k-1

A: We know that the combination formula: C(n,r) = n!/(n-r)!r!

Q: 3 5 If f(x) = 2 – 6(x - 1) +(x – 1)2 – ¬(x – 1)3 + 2! 3! 1 -(x – 1)“, what are f"(1) and f'(1)? 4!

A: Given that, fx=2-6x-1+32!x-12-53!x-13+14!x-14 Then we get,…

Q: #8: Suppose that an = as 8n a₁²2² +2a₂x³ + 3a3x²4 + 4a4x³ + ... (i) Σf(n)x"+2 n=0 (ii) g(n)x+1 We…

A: This is a good exercise in summation and we shall see how to change the indices.

Q: 1 3. lim 8 (t5 + 1)2

A:

Q: 2 13) Consider f(x)= x<o 12x+1 0≤x≤2 Determine whether f is continuous on [0,1] and [1,2]

A: solution of the given question is like as:

Q: 9- Let X-U(0,0), then P(X> X²) is (a) 0 (b) 1/0 (c) 1/2

A: Given that, X~U(0,θ)

Q: lim (8n² – 7n – 500) = – In³ -

A: The rational expression 1xq can also be expressed as 1xq=x-q. We know that limx→∞ 1x=0. We also know…

Q: Let n EZ. Show that f(x)= x³ – nx +2 is irreducible over Q for n+-1,3,5. 72

A: Given: fx=x3-nx+2, n∈ℤ. To show fx is irreducible over ℚ for n≠-1,3,5.

Q: and g(x) = x³ g(x) for all x, if gls) = 4 find 9" (5) = 4 and

A: Given, g'(x)=x3g(x)g(5)=4

Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where is player i's…

A: The utility to player 1 is given as: u=xx+n1yAnw-x-n-1y;w&gt;0,A&gt;1 Also, Ak=Aw-x*

Q: 73. y" + 3xy' + 3y = 0. (-3)*x²47 y = a[1 + 2 (-34 x²] + a ₁ x + 2 ₁ 3.-5.-7. (2k + 1) ! ANS.…

A: Given y"+3xy'+3y=0

Q: 5 2 7 . If f(x) = 3 + 4x · 2* + r", what are f"(0) and f"(0)? 3!

A: Given f(x)=3+4x-52!x2+73!x3

Q: 2. Let f(x) = -x– 1. a) Find f-1(x).

A:

Q: Xi lim Σ n18 i=1 (x)² + 4 Δx, [1, 3]

A: Write integral as limit of a sum.

Q: 2 In R show that 2 2 2 @ 2 11 × 11 ²2 + 2 ||1y|11² = 11 × x + yll ² + 11 × -yll ² (Parollelogrom Lou…

A:

Q: k* for some constant k". Lp.) Show that L(po)

A:

Q: Determine the domain of 3+ x1/3 - 2 f(x) = х- 1 A [-27,1) (B) X2 - 27 [-27,1)U(1, + ∞ D [1, + 0)

A: We have to solve

Q: - Consider the open statements: P(x):x = -2 and Q(x):x² = 4 over the domain S = {-2,0,2}. State each…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: 5. Let h (z) = (z+1)(z+6)(z+10) z(z+2)(z+3) (z+3)(z–2)°, (z+2)(z+6) What is the residue of h (z)at z…

A: Given a function on complex plane as hz=z+1z+6z+10zz+2z+3+z+3z-22z+2z+6 Residue at z=-2 is given by…

Q: Evaluate the following sums: (i) Σ(k + 1)x*, |x| < 1;

A: ∑k=0∞k+1xk,      x&lt;1 Note: There is three different question, according to the guidelines we are…

Q: 4. (a) Let a : Z→ Z be the function defined by a(n) = 2n + 1, and let i: Z → Z be the identity…

A: