Q5: For which values of z is w =1/(z – i), defined? For these values obtain and v and evaluate w when z = 1- 2i.

Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: Q4) ut A = :) al let fox)- 2x_4x+5 and g(x)= x?42x + 11, Fiind + 2X + 11, Find @ A ; DA ; © PCA);…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Let T: RP → R be defined by T() = Aã where -2 3 11 A = 1 -2 1 -1 -3 4 and let 6 %3D What is the…

A:

Q: Q4/ if f(x.y)=x-y and g(x.y)=3y prove V2) gVf-fVg g? %3D

A:

Q: Q2) f(x,y) = 2xy x(s,t) = 3s-2t and y(s, t) = s²+4t. Find Je Je as at

A:

Q: əz Let z=xln(x2+y²-e*)-61xy, x=te°, y=est. If the value of when s=2 and t=1 is equal to Ae?+Be4,…

A: Partial Derivatives.

Q: If f(z) = (iz? + 3z?)³, find f'(z), when z = 2i. %3D

A:

Q: d) Let y= Acos2t where A is a constant. Find the value of A such that d y --3y = 9cos2t for all…

A: Given  The equation is  y= A cos(2t) , where  A  is constant  and condition is  d2ydt2-3y=9cos(2t) .

Q: Let f(2)= ¹5 and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of…

A:

Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: calculate SN given by Simpson’s Rule for the value of N indicated.

A:

Q: (c) For any (a, y) E R?, let F(x, y) = (4x - 3y + 1, 3x +4y + 1). Then F is a similarity.

A:

Q: Q/ Let X be the r.v such that E (X) = 2 , E(X²) = 2a , E((2+aX)²) = 2a³ Find the value of a

A: We have given that, Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)²) = 2a3 We want to…

Q: H In OJ, GH = 9, KL = 4x + 1. Find x. R 5. 5 S. GK

A: Given: GH=9,KL=4x+1  If from a centre a perpendicular is drawn to the chord, then a chord is divided…

Q: Find V²f by the formula V²ƒ =div(grad f) given f(x,y, z) = e³wyz grad f = [| V²f =

A:

Q: H.W.3: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate…

A: Explanation of the answer is as follows

Q: _1. Differentiate the following w.r.to x (i) V(x? + 1)3 .3,-2x (ii) + In (3x + 1)

A: Using derivative ,

Q: In r e) I/1+ (In z)² dr

A:

Q: (a) (x² + y² + z² + w?)3/2 = 4

A:

Q: Q2: Let XN B(4, 0). Let H, : 0 = and H : 0 = . Using the definition of BCR, find (1) a BCR of size a…

A:

Q: Q5.Given that W = f(x.y.z)% x+2y+, find : aw aw in terms of s and r, if and x=, y=r +Ins, =2rr.

A:

Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

A:

Q: p* + 51³ + t² + 5t + 5 -dt = 1? +1 (Type an exact answer, using t as needed.)

A: NOTE: Refresh your page if you can't see any equations. .

Q: e) Use (; a²p Find the value of Vm at which both of these deriva- T to find aVm tives are zero.

A: I will present e bit for u in the last step....inorder to show u the steps clearly of e bit , I have…

Q: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)²)= 2a3 Find the value of a .

A:

Q: Q3/ Find length of the cardioid r-a@3from 0 = 0 to 0 = n %3D

A: The equation of the cardioid is r=aθ3. The length of the cardioid is given by the formula,…

Q: The mgf. of a r.v. X is (}+3) (+e) . Show that 9-x Ρ(μ- 2σ<X<με 20 - Σ (!) ( (3) P (μ- 2σ< <μ+…

A:

Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

A:

Q: Find a, b > 0 such that the following equality holds: {r €R : -a < br – 3 < v2} = [-3, 3).

A: Note the result : The set can be represented in interval form as .

Q: Find the I-coordinate e a Hhe ocal monimeno 07 local makimum of 7 qunction n 7ux)=e? (2x²+3x), x ER

A: Second derivative test : Suppose f is continuous  and differentiable function at x=a where f'a=0 and…

Q: Find Duf at P. f (x, y) = 3(1 +wy)"; P(1,3); 1 1 i+ j V2 u = NOTE: Enter the exact answer. Duf ||

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: (ii) Assume that d = in E-coordinates and 7 in B-coordinates. y' Find a' and y' expressed in x and…

A:

Q: Find Duf at P. f (x, y) = 3(1+ xy)/"; ху)"%; Р(3, 5); и%— 1 1 i+ j V2 u = NOTE: Enter the exact…

A: Given function is  f(x,y) = 3(1+xy)3/2 and point P(3,5)  And u= 1/√2i+1/√2j  We have to find out the…

Q: ( b) For n=1,2,K , show that (x² –1)y"*) +2(nx + p)y") +(n² –n)y"-1) =0 where %3D d" y p") = (Hint:…

A: * Given that y = x+1x-1pa dydx = px+1x-1p-1ddxx+1x-1    dydx = px+1x-1p-1x-11-x+1.1x-12   dydx =…

Q: Using the Method of Substitution, evaluate : 54х dx (1 – x2 O 54 /1 – x² + C, Where C is the…

A:

Q: Q5: For which values of z is w =1/(z - i), defined? For these values obtain u and v and evaluate w…

A: Given that: w=1z-i, z=1-2i

Q: Q9. If W = f(u)=u' + sinu+Inu, and a=ax+by, where a, and b are constants, show that aw aw b. ax

A: We have to prove the given statement.

Q: Q3/ Find length of the cardioid r=a03from 0 = 0 to 0 = t %3D

A: By using length formula we find the length of given cardioid as follows :

Q: メpr t! prove that : d = (s«k-tank)

A:

Q: x'y=x'+ xy. linear DE Which value of k, the given DE will be homogenous?

A:

Q: Exl Let c R,Z) be usual toP s Pace and A-fcxy)ER/ x²+y²< 13 find A Ext CA), Ā , A°

A:

Q: a) (dx pcG) V ZxqG))3x (pG) V96), Pore this bis the converse of t he implication above correct!

A:

Q: Find all values of x so that v · v = 1, where

A: Given vector, v=12-12x That is v=12i-12j+xk

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

A:

Q: Q1 In the fellowing table find Z CG) ,ccal all a E G to

A:

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

A:

Q: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+aX)²)= 2a³ Find the value of a.

A: E(X)=2E(X2)=2aE((2+aX)2)=2a3

Q: Q1. Consider the two different losses: (i) zero/one loss where Ai dij = 1 and (ii) generic loss…

A: Given Consider the two different losses: (i) zero/one loss where A₁ = 0 and Aj = 1 and (ii) generic…

Q: 10 Q5/ Evaluate x*dx ,n 5, using trapezoidal rule.

A: The trapezoidal rule formula is: ∫abf(x)dx≈∆x2f(x0+2f(x1)+2fx2+...+2fn-1(x)+f(xn))...(1) where,…