Expand: y= In O y = 6 lnx – 4 In w+3 Iny- In z Oy =6 Ing – 4 In w – 3 Iny + In z Oy =6 Inz +4 In w - 3 Iny- In z Oy =6 Ing - 4 In w+3 Iny- In 2 Oy = 6 In +4 In w-3 Iny-In 2 Oy=6 Ina-4 In w-3 lny+ In z

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A: Given, Let z=f(u,Y) u=ax+byY=ax-by

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Q: The linearization at a = 0 to /3 + 9x is A + Bx. Compute A and B. A = B =

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A: Here, one matrix function, A=1-223 is given Let the X=a1b1a2b2 So, X¯=AX=a1b1a2b2.1-223…

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A: Consider the given equation.

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A: Given that Diffrancial equation y'x+2x2+44y=2x415y4To find : integrating factorSolution…

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

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Q: Let y1 = 9cos(2x) and y2 = 2cos2 (x) – 2sin? (x). Calculate the Wronskian, W(y1, Y2). Give your…

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Q: verify that (A + B)T = AT + BT

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Q: Exercise 4 Show that for cach k EN it holds that kn-k < n! S n", Vn E N, n2 k. Deduce from this that…

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Q: (a) Let f(r, y) = -2r*y² – In(y²). Compute fyzz (b) Let g(r, y, 2) = 1(3y* – 52²). Compute

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Q: The linearization at a = 0 to v4 + 4x is A + Bx. Compute A and B. A = B = %3D II

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Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

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Q: EX: Find the Z. T. of X(X) = cas wok u(k) 8 iwok -iwok Sol:- X(Z) = - IN Σ coswok. Z k=o == {(² z ¹²…

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Q: prove that F(r) = 4z-3z is chaotic on the interval [-1,1]. (Hint: consider g(6) = 30 on S'.)

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A:

Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

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Q: Assume that u = U (x,y) iu differentiible and x =r ca Ô and y=rsin o eapress 2. entinely in termv 0…

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Q: Evaluate the given integral applying Chain Rule * S(V25 + x² ) 2x 2 (25+x²)v25+x² -+ c С. 2…

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Q: Solve for x and y the followinglsystem of simultaneous equations 2 In(x) = In(y) + In(4) e*e = e?…

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Q: If f(z,y, z) = I COs(2y – 2). compute and af and Te Əz =I Cos(2y -2). compute O = cos(2y2) I sin(2y…

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Q: Buuton 5: Expect alion and Varian ce Let X fe a oontinuous pan dom van'able and Y: a X + L you some…

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Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

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A: Given,           f(x,y) = lnx2y3,  where x = s2 + t2 and y = 2s + 3t

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Q: (1) xyy' + y² = 2x O separable exact O linear in x O linear in y O homogeneous Bernoulli in x…

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Q: Let X and Y have the joint p. d. f . sx+y if 0<x, y < 1 elsewher f (x, y) = %3D The covariance…

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Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

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Q: ☺ RB=R defuid by T☺)- matria "A" it. T@)- A:). つレ- TV4 Let T: -3v-Jw ). Füd

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Q: Evaluate the integral. |csc 37t dt 1 O A. 1 csc 7t cot 7t- In |csc 7t + cot 7t| + t + C В. 14 csc 7t…

A: givenI=∫csc37tdtrewriteI=∫csc27t.csc7tdtwe know trigonometric…

Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

Q: Poblam cu (a) Compute Cm 2月-/ where xe [-,]. (1) 2n 2n-1 where ze C-1,1]. (b) Gompule Cm z nっ%

A: (a)

Q: F. Boolean MIatrices 1 0 1 [1 1 17 To 1 Let B = C=0 1 1: D=0 0 1 0 1 0 100 [1 0 [1 0 0 1 E=1 0 1 0…

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Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

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Q: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

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