Prove-that '(2) r' (₂+1) ¹ (2+ |) T(₂) nd thus derive Legendre's duplication formular 2' (2) T(2:) 2log 2

Q: A) L{t//4} : (5/4)! a+5 B) L{u-2(t)} C) L{e"u(t)} 8- 5 3! D) L{t*e"} = E) e{icm (;)} 5Cos s(s – 2)…

A: A is false  B is false  C is true  D is false  E is false  The detailed solution is as follows…

Q: Find Oz/ou and oz/ov for z=4e* ln(y), x=ln(u cos(v)), y = usin(v) at the point (u, v)=(2.7/4).

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Q: Find the coefficient of x10 in (1 +x+x²+x³ + •..)" Find the coefficient of x' in (x +x6+x² + • ·…

A: 1)Given expression1+x+x2+x3+....nThe series 1+x+x2+x3+.... follows a geometric progression with…

Q: L[u(t – 3) (1²4' – 9 4')] = 81e-4s 2 (s-ln 3)3 8 (s-ln 3)2 64e-3s 2 (s-In 4)3 6. (s-In 4)2 81e-4s 2…

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Q: 9) How many roots (zeros) does f (x) have? a) 0 b) 1 c) 2 d) 3 e) 4 10) How many extreme points does…

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Q: 2 - Jx - 3 – v 4) lím エ→7 x² – 49

A: Given: ⇒limx→72-x-3x2-49

Q: If pq > 0 and the roots of (x' + mx + m = 0 are in the ratio p:q then equals (a) 1 (b) 0 (c) (d)

A: We know, lx2+mx+m = 0Let,p, q be the roots of the quadratic equationwe know that,1. p+q = -ml2. pq =…

Q: 2 4) + +2 +2

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Q: If 2x² + 3/xy – 2y + 4 = 0, then y' at (2,2) =

A: The given equation is: 2x2+3xy-2y+4=0 Differentiate w.r.t x to get:…

Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: 5.Jf(x) =- 3x + 7 g(x) = 2x - 8 Find f(g(x))

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Q: Vr+2+Vx-2 If a = prove that a -ax +1=0 Vx+2-Vx-2

A: To prove , we need to simplify the left hand side of the equation till it becomes 0. To do this…

Q: (10') Use Rouche's theorem to find the number of roots of 2z4 – 5z + 1 = 0 (1) for |z| < 1 (2) for…

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Q: 13 4e 6t -3t x; X 28 - 10 7e 6t 4 e 3t 13 4 13 -4 6t 4e |=x,' 28 10 28 - 10 7e 6t

A: The given question is solved below.

Q: Find Solution of Homogeneous linear ODE s (D°, 60 +131 Jy

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Q: Q) Find an approximation to one of the zeros of p(x)=x3-2r2-5 using Newton's method and synthetic…

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Q: not Show that ([0,1]_is in the l' metric d (fig)= (51f6)-96) ³d x) ² fumpluts

A: The given set is X = C[0,1] and the metric defined on X is L2 metric which is defined as  df, g =…

Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

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Q: erfind the first agd decond derivatives oh the funchan

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Q: 4. a) Solve the equation 5sin-'x- 2n = 2sin-'x-3n 6) Graph, find x where f(x) = g(x), bounded by…

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Q: Show by two methods one algebraic and one combinatorial that: ΣΗ (E) (-) = (m*") -k=0

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Q: Find u, v, and ||u + v||. 4, (a) ||ul| (b) |v|| (c) u + v 'T) = A

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Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

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Q: Find all the value of (-8-8√31) 1/4 and (2+2;)²½/3

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Q: -2) Calculate A-1 by 2 Let A = 1 2 1 -1 -1 A-' = ÷(-A² + 3A +I). and verify your result by showing…

A: Given: A=12-2121-1-10 Therefore,…