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: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

A:

Q: b) 4(x – 4)(x + 2)² (2x – 1)³ < 0 - -

A:

Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

A:

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Show that z / [(z-1)(z-3)] = -3 Σ [(z-1)n / 2n+2] - [1 / (2(z-1))] for 0 < |z - 1| < 2.

A: by using techniques of partial fractions and series expansion of 1/(1-x)

Q: In(1+ 5.x?) 2 – 3x Differentiate with respect to x.

A:

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…

A:

Q: Find x, y, z, and w. x y z 8 (x + 7)] = [ (2² (2x - 3) X -1 W (9 + y) -8

A:

Q: Suppose that an = 4" a₁x² + 2a₂x³ + 3a3x4 + 4a4x³. as 00 (i) f(n)x+2 n=0 00 (ii) Σ g(n)x¹+1 n=1 00…

A:

Q: 6. (x – 1

A:

Q: 6. Use a substitution to find S (x* + 1)" z³dx.

A: Here we use substitution we find∫x4+111x3dxHere we substitute x4+1=du…

Q: evaluate L-1 { t/(s-2)(s+3)}

A: By using partial fraction and table of Laplace transform we solve the given problem as follows :

Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β&gt;0 and q&gt;3.…

Q: Q.4) Find the value of Sigma (d=sum of student id + 22, and c=12) 4c(d + x)(7c* +2cz +9z*) ((d +x)*…

A: As the student ID is not provided, I assume the sum of the digits are 10 (say). Then d=10+22=32 and…

Q: dx (1)(- 2e * )

A:

Q: *) Let p(x) = 8x – 7 and q(x) = /x – 7. Find u(x) given that q(x) = p(u(x)). - и(x) —

A: see 2nd step

Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

A:

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: & 18) Vaing showj that the idently in

A: Using the identity 1+x2n=1+xn1+xn,                . . . (1) we want to show that 2nn=∑k=0nnk2.…

Q: if z=x+iy find real x and y such that |z+3|=1-i(z-2)

A:

Q: Ž ( – 1)"x" 1+x

A: Given the power series

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: and (A) (B) = x, = 2x, = 3x, Show that if 8. N N (AB) _ (BC) _ (AC) 1 = y, then the value of neither…

A:

Q: 4- (a) Show that XYX = -Y and (b) show that [XY,YZ] = -2iY.

A: a) To show that XYX = -Y, we can use the definition of the commutator [X,Y] = XY - YX and the…

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

A: