1. Prove L = re L 0 r

Q: i. If n is positive integer, Find (√3+ i)” + (√3 − i)”. ii. Separate tanh-¹(x + iy) into real and…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 3. Evaluate || (3y+ 2x“) dA, where R = {(x, y) E R² : |x|+|y| < 1}. R.

A:

Q: b) I =f- x(1+(In x))

A:

Q: 4) Evaluate ĺ jedydx 29f071p =

A:

Q: B. Suppose that y1, Y2, ., YnidN (0, o2). We wish to find the most powerful test for Ho:02 = o3…

A:

Q: Prove that fVf · dr = 0.

A:

Q: 15. Calculate (41 + 3, r?. –4r³)dt.

A: To calculate: ∫034t+3, t2,-4t3dt Solution: Power rule of integration states that: ∫xndx=xn+1n+1…

Q: , Giran me qiven family of ines for b=0, I, I 3, I6

A: Graph of  y = -2x y = -2x -1 y = -2x +1 y = -2x -3 y = -2x +3 y = -2x -6 y = -2x +6

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

A:

Q: prove that l+2 +3+.. +h = n(ntl) for n=1,2g3 2 %3D

A: Given :               1 + 2 + 3 + ... + n = n(n+1)2 Let P(n) :               P(n) = 1 + 2 + 3 + ...…

Q: If m and n are positive integers and w = g(x"y"), then show that dw dw = my dy

A: Given w=g(xmyn).

Q: Let n 22. Prove that the equation y" = 2r" has no solution in positive integers.

A:

Q: 3. For Z= xtanxy,evaluate Zyy

A: The given function Z=x tanxy We have to find Zyy.

Q: II. Evaluate the following. 1. z = ji

A: Given: z=jj

Q: 2 and y = If x:y:z 4:6:9 and z = 45, then x =

A: Given:          x:y:z=4:6:9     and   z=45To…

Q: TF x and y are orthon ormal rectors then Pind Value of Ilx+y12 - ||x-Y2

A:

Q: 13. Prove or disprove: Q/ZQ.

A: (.) We have to prove or disprove .

Q: Cannot solve

A: Given

Q: L [1\ucos Puf) Ju

A: 1st we will find value of integral using integration by parts and then use Laplace transformation…

Q: b) Consider the second-order DE. y" +25y = 0 rE (-00, 00) Show the zero’s of the solutions separate…

A: The given differential equation is y''+25y=0 If D=dydx then equation will be D2+25y=0 Now Auxilliary…

Q: Set X = x 0 1 Y where x, y are unkonwns. Solve the equation X² = 10

A: given and

Q: cothiz-l=eschz

A:

Q: Find the first 3 iterates using x² = x + y² y(o)= o` Successive Approximatio

A:

Q: 5. (BH) Calculate det B, where 0. 4 1 1 В — 1 -2 4 -1 2 1 -1 0 7

A:

Q: 6. Find a line parallel to 3x - 2y = - 4 and passes through (4,-2)

A: We know if lines are parallel then slopes are equal  Given line equation is 3x-2y=-4

Q: 17. Let a, = (-1)" vn 2 1. Calculate the value of an+1 - a, for odd values of n. A.-1 В. -2 С. 2 D.…

A: Given sequence is  an=(-1)^n

Q: tnd if Zi=ñ Ccoro tisino] and %3D

A: z1=r1cosθ+isinθ and z2=r2cosϕ+isinϕ