11. Given: WX||YZ; XY||ZW Statements Reasons Prove: AWXY = AYZW Y 3. Z. W

Q: Let f(z) : sin(3z) %3D and C: |z – 9| = 1. Then ſ. f(z)dz = %3D - z2(z-n) a. 0 b. 2ni с. 9 d. None…

A: Cauchy Integral Theorem: If a complex function f(z) is analytic on a simple closed curve C . Then ∫C…

Q: Check it for f(x, y, z) = x²y°z*, that is, compute Vf first, then V x (Vf).

A:

Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) f(x,y) (c) Syy(x, y) (d) fyz(x, y)

A: Given function is f(x, y) = x sin(xy)

Q: Find J, ()dx Chint:let Z=Jx)

A:

Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: Calculate , if xyz Ax, y,2) = x² – x²y³ -2 3 = x -x y -Z A.5 1 C. No one correct. В. D. E. 7 Е.

A:

Q: Give the condition which ensure that Je-| < 1 where z E C.

A:

Q: XY 1 VY, XY | VW, and WX 1 VW. Complete the proof that AVWX AXYV. W Y Statement Reason XY 1 VY XY ||…

A: Given:

Q: Evaluate F.dr where c is defined by r(t) =; 0≤t≤ 2π

A:

Q: re 'C' is z-

A:

Q: H.W 1- If P(X = 0) = 0.2, P(X = 1) = 0.3, P(X = 2) = 0.5, P(Y = 0) = 0.4 and P(Y = 1) = 0.6.…

A: Given: PX=0=0.2PX=1=0.3PX=2=0.5PY=0=0.4PY=1=0.6

Q: 25. Which of the following is the answer for secx = V2 A. E + 2nk|k E Z}U {+ 2rnk|k € Z} 3 B. G+…

A: We will solve the problem

Q: Let w = f(x, y) with f E C² and x =h – kh, y = 4k. Which of the following statements are true?…

A: To find  Which of the given statement is true.

Q: Let f(x, y) = x(y - 3) and F = Vf. If r = with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c.…

A: We find the line integral in the following way

Q: 3. Find the coefficient of xy' in (2x + 3y)°.

A: The provided information is we find the coefficient of  x2y7    in (2x+3y)9 Then, (79)*(2x)2*(3y)7…

Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

A:

Q: Which of the following expressions are not valid? Why? (a) [ f* 1(x, y) dy dz [T (c) [[1(x, y) dy de…

A:

Q: 19 5. Evaluate F. d R where F = yî + xz°j– zy°k, C is the circl x? + y? = 4, z = 1.5 Ans. TC C 2

A:

Q: Let f(x, y, z) = 4xy sin (yz) and F = Vf. Evaluate feF. dr, where C is any path from (0, 0,0) to (9,…

A:

Q: If |z-8 <, and ly-히 < , then a - y < 1. 2'

A:

Q: 7. Which of the following is a wff of P? Circle your answer. (a) Jvb (b) (3y)(Sy → Sx) (с) (x)(Нх Л…

A: WFF is the abbreviation of Well formed formula which follows certain rules The letters should be…

Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

A:

Q: - Classify the following lines as parallel or perpendicular or neiti a- y=4x-7 & y=4x+9. b- y=-5x+1…

A: Given: a. y=4x-7  and y=4x+9b. y=-5x+1  and y=3-5xc. y=12x and x=12y Concept Used: Two lines are…

Q: Show V(X)

A: The joint probability mass function of X and Y is  f(x,y)=(x+y)/21   , x=1,2,3 and y=1,2

Q: se se fe and az ryz 1. Let f(x, y, z) then find the value of %3D x+y + z ax' dy

A:

Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) fy(x, y) (c) Syy(x, y) (d) fyr(x, y)

A:

Q: None

A: Step 1:Step 2:Step 3:Step 4:Step 5: Else anywhere, no common area hence A=0 Step 6:

Q: - X1,·… , Xn i.i.d. Uniform(0, 0). .. Find X(1)+X(2) ] E

A: