Q11] Integrate counterclockwise around C. Show the details. sin3z 1) ,C:Iz| = t z2 5z3 2) ,C: Iz| = 3 z2+4 5z3 3) ,C: \z – il = ni z²+4 25z3 4) ,C: |z – 5| = 1 (z-5)2 5) ez, C:|z – 1- i| = 2

Q: 4. By using Cramer's rule, find the value óf Y: 2x +3y-2=16 5X-y +2Z = 36 X + 2y -42 =5

A: We have given that  2x+3y-z=16 5x-y+2z=36 x+2y-4z=5       In matrix form  23-15-1   212-4xyz=16365…

Q: Find the branching points of the given complex functions a) f(z) = vz+ vz– 1 b) f(z) = vz² +9

A: A branch point of an analytic function is a point in the complex plane whose complex argument can be…

Q: 5. Let z1 = a1 + b;i and z2 = az + bzi. (a) Find Im[z,Zz + (Z)? – 2,7 ]. (b) Prove that (z)² = z,² .

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: x³y' +3x?y" +xy' +8y=xInx Select one: a. YG.S +x(c2sin3lnx+c3cos3Inx)+x ( Inx -) - Inx: b.…

A: Given equation is  x3y'''+3x2y''+xy'+8y=xlnx            (i) Let x=et. Then…

Q: Q2. Consider the ODE Using u = y ¹, we get A) u' - xu = sin x B) u + 2xu = - 2 sin x C) u + xu = sin…

A: The given differential equation is       y’ - xy = y2sin x    . . . . . . . . . . . . (1)    Now, we…

Q: J32 For z = cos(x-4y) show that # дудхду 332 дугах

A:

Q: D2-2D- 3)y = 2sin x; y a. y = C,e™* + Cze* - cosx -sinx %3D COSX b. y = C;e¯* + Cze³* + =cosx – sinx…

A:

Q: 0/ifit was FCかy)2165(6w)30 2 -36 y? cos (6XY) .3 =36 Y'cos (6X4) -36 y'cos (6xY) 2. = 36 y'cos (6XY)

A:

Q: əz Use Chain Rule to determine and where

A: We have to use chain rule step by step.

Q: ulo,3) = 1+ y 1) u'xg U(x, o) = 1+x 2

A:

Q: 5. Find Wxxyyz, Wzyx, and მაw Əzəx²ǝy² if w(x, y, z) = x³y-5 + sin(xyz) + In(x + yz). C

A: Note: All partial derivatives are not small. I can solve only first two partial derivatives as no…

Q: If y=t3, then y(6)+y(5)+y(4)+(1/3)y'=y? What is the power of y? a) 0 b) 2/3 c) 1/3 d) 3 e) 2

A: Differentiation of y with respect to t can be given as:

Q: 2 a) y = Find y'. 3e (ax-5)4

A: Explanation and solutions is given below.....

Q: Show that if Y = ax + b (a = 0), then Corr(X, Y) = +1 or -1. We know Cov(X, Y) = Cov x, ])--)-I + b…

A: We need to show that, If Y=aX+b then Corr(X,Y)= +1 or -1

Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

A:

Q: 2x (x-6) 3.) y = (x-3)3 required:a) yand y"

A:

Q: əz ax+by+sin(ax +by) show that b əx Q5-A) If z = (ax +by)² +e+by+sin( ax a Əz dy

A: The given problem is to show the following condition for the given multivariate function of z.

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

Q: If  u=sin(x+2t), then (∂2u/∂x2)=(?)(∂2u/∂t2) What is the coefficient of (∂2u/∂t2)? a) 2 b) 1/2…

A:

Q: 2. State the leading coefficient, degree, and symmetry. [K/U 6] b) y= e a) y=3x-4x² + 2 -6x c) d)…

A: Given: a) y=3x4-4x2+2Leading coefficient=3, degree=4 and symmetry=y-axis

Q: 2 a) Solve x y'= (2+ yx)·

A:

Q: bj f(x,y)= еху cЈ fexiy>= x cosx cобу p² d.j fexiys= (x'y 2) log (x'ty ?).

A:

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

A:

Q: Find the value. 11) If F(x, y) = -9x+4y, find Fx(-4,-9) and Fy(-4,-4), xy A) Ex(-4,-9) = 1,…

A:

Q: 3T/4 18) 3 sec 0 tan 0 de

A:

Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: 1 3 For V Vy evaluate y' when y = 4. A) 4 B) -4 C) -2 D) 2

A:

Q: 4. Find_r(t), if_r'(t)=4sin(2t)i +8t³j and r(0) = 8i-3j. A) r(t)=-2 cos (2t)i+2t¹ j B) C) r(t)=-2…

A:

Q: 1 b)y" + y = ; 1+sinx

A:

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r — cos (t)), (r, t) = =(5,2)…

A: Jacobian of the function

Q: 10. f(x) =-x2 +3x+ m, y 4-IOBI = 10CI %3D A(ABC) = ? B.

A: As per guidelines, we will solve first question poste. 10) Given fx=-x2+3x+m 4OB=OC