4. Demonstrate that Re(iz) = -Im(z);

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: 0 2 4 6 2 3 4 5 If A = Compute C1(A). 2589 3 2 1 7

A:

Q: If U(x,y)=In(x²-y³) then Ux+Uy= ... XX

A:

Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: (a) Show that xn → x and Yn →y implies Xn + Yn → x + y and also show that an -→ a and Xn → ax. → x…

A:

Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

A:

Q: y = In(In 2x)

A:

Q: 6. y = 5e* +3

A:

Q: /9 – 2° dz Integrate: z4

A:

Q: 1 If z = 2 V3 -i, then find ()*

A: Given complex number is: z=-1-3i2 Find the conjugate of complex number: z¯=-1+3i2 Find z¯4?

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

A:

Q: xy If z show that: x- y

A:

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2. Solve the given SLE using LU-Factorization X- X, +4x, = 4 2x, +3x,-5x, = 0 .

A: x1+x2+x3=3x1-x2+4x3=42x1+3x2-5x3=01111-1423-5x1x2x3=340Now, A=1111-1423-5, x=x1x2x3,  B=340

Q: 3e dt 10. SET A.

A: We will use the concepts of definite integral

Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

A:

Q: 1 Show that xn-m)}-2X(2). assu me. Zera 1c

A: As per the company's rule, we are supposed to solve one problem or three subparts. As there are two…

Q: 3-Evaluate S Fdr where 2X Cisgiven by rT) = C 3+U-3t)jrék

A:

Q: 12 y' (12x +5) (4y* +3)° b. If y* +3y-4x' = 5x+1, then prove that y"(4y +3) = 24.x--

A:

Q: Suppose z = 1+ li. Then |z| =?

A:

Q: Suppose that X and Y are unknowns with E ( X ) =12 and E ( Y ) =20.  If E ( XY ) =225, then what is…

A: E(X) = 12 E(Y) = 20 E(XY) = 225

Q: 13. - (In t ² )º t dt

A:

Q: 42. Show that S 4xys + %3D 1- x2 1- y? 1– 22 (1 – a²) (1 – 3²) (1 – 2²) if xy + xx yz = 1

A: Given that  xy+yz+xx=1 Prove that the expression

Q: If U(x,y)=In(x²-y³) then U+Uyy= ....... ....

A: The solution is given as

Q: 2 Evaluate: ²₁²(x²-y²² du dt

A:

Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: In 3 e'dt Je2t + 100

A:

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: az If x2 + xy + yz + z2 = 6, then- ду

A:

Q: If In(ax)dx = 2, then a = %3D 1

A:

Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

A:

Q: c). Invest diFrgate whether the given en equation is homogene eous dy 2. oxy

A: A first order differential equation is homogeneous when it can be written as a function of y/x, that…

Q: In GL(2, Z,), the inverse of Option 4 (2 10 O Option 2

A: we know that inverse of matrix A= 1/|A|(adj.A). see 2nd step.

Q: 4-5. Evaluate the Integral 31) dt

A:

Q: What is the best substitution to make to evaluate S O u = 3x Ou = e³x u=1+e³x Ou = e-3x e³x 1+e³x dx…

A:

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: JJ. JUA X ABD) 224 ABE) 16 36. g(x)=2x -3x² +5x+3 ACD) 1 АCE) 2 37. h(x)=x -4x³ +3x² +8 ADE) -3 BCD)…

A:

Q: Show that S ťe dt = 3VI

A:

Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

A:

Q: 2. 1. If UZ = x+ 21 and ZS = 3x – 15, find US.

A:

Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: 13. If w(x,y) = In(1+xy²), show that 2wxx + y³Wyx = 0. %3|

A: Given: w(x, y)=ln(1+xy2)  To show: 2wxx+y3wyx=0 Chain rule : ddx(f(g(x))=f'(g(x))g'(x) Quotient…

Q: Suppose that X ~ Unif(-1,1). Compute (d) P(X = 0.5), (e) P(X² > 0.5).

A: Let ,  The pdf of X is ,  = 0 ; otherwise Our aim is to find the following :  d) P(X=0.5) e)…

Q: EVALUATE S(3sin t - 2cos t) dt

A: Topic = Integration

Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.