(z – 4ŋ³ at = 3 + 4i

Q: Q4 If f (x, y) = x sin y + ey asf ax2ay3 Find

A: Let's find.

Q: (トタりナーそJ0 on メou sqo とてラメテ0 'hらトラメe 1(h8)3-9 4 トtト×ピーメピ(トタ)さーそ ト×-メと -(ドメ)きーモ

A:

Q: R m 1 Uo 1 2Tr dr TR²

A: Follow the procedure given below and use simple integration principle.

Q: f (t) = 3e" cosh (In 2r -2t

A: Given,                 f(t)=3e-2tcoshln2t

Q: cle below, suppose m JIL =274° and mLIJK=111°. Find the follo J K (a) (b)

A:

Q: dx If - = Sh(8) d®, then h(0) de = ... V(4+x2)3

A: We will make use of only the basic techniques of integral calculus to solve this question.

Q: Find the B.C.R let XXgg, Xn vN (@,1) H:0-2

A: We have to find the best critical region which we will find by using neyaman Pearson lemma.

Q: Q4/ B/ If Ø = (x³y²z) and A = 2xz i - 3y²j+ 3xy²k Find 0(ФА) ay əx the point (2, -1, 3)? at

A: Given: ∅=x3y2z and A→=2xzi→-3y2j→+3xy2k→  To find: ∂∅A∂y∂xat the point 2, -1, 3 To solve the problem…

Q: 5. Show that T = + y? satisfies the equation T + Tyy = T³

A:

Q: dy 1. If a? + e 2xy = r + (y-2), find when r 0. dr2

A: We have to find second derivative at x =0.

Q: Q4) Choose correct answer : rtan-(cotx) dy dx = i) So 10n а. 44 15n b.- 44 20n С. 44 d. 1-n 2

A: Given: ∫01∫0tan-1cotxdydx

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: z= em and a = 2t– 2s?, y = 2s – 2t, find az at t = 1, s = 1. at

A:

Q: d? -(A+B) at t = 1. di?

A:

Q: find the corresponding x to the z1 value from P(z < z1)=0.1056

A: Let , X→N(μ=29.3 , σ2=169) We have , P(Z&lt;z1)=0.1056 We want to find the value of x corresponding…

Q: 3. If GH = 7x + 18 and JK = 81, find x. %3D H G 丰 K %23 世

A: In this question given that two triangles and both are same . Their sides are same and we can say…

Q: dz where C is ned by x = 0, :

A:

Q: Using WXYZ from the previous question, if WY = 32, find XY. %3D

A:

Q: if dx =3 then k =2e3 %3D - Select one: True False

A:

Q: Q/ Find SCZ)dZ Where C:\z-1|-l

A: We use Cauchy's Integral formula.

Q: dz where c is |z=1 z'e? Evaluate

A: ∮ f(z) dz = 0 when no any singularity lies within region of integration. But if any singularity lies…

Q: -dz < 2re?. z + 1 Jェ-1|=1

A:

Q: d) solve to 1l o wing equan on. the differenti al 2 dy 3y = 3 n2 + 5 %3D

A:

Q: 80. If x? – y? = 1, find d²y/dx² at the point (2, V3).

A: Given: x2-y2=1 at 2,3

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: ds Find dt S=- 3tan t-et

A: Given, s = -3tant -e-t   We have to find the value of dsdt

Q: Find the value of the secant for ZR. 3)14 14 а. b. V5 с. d. 3 R O A

A:

Q: Find r'(t) r(t) = 8/ti + t?Vij + In(t² )k

A: We will solve the following.

Q: У(2x? — ху + у?)dх — x? (2х — у)dy %3D0;B у(1) - H IN

A: Use homogeneous equation

Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

A:

Q: (xiv) f(t) = 3+et – te-2t + e5t cos3t + 6sinh7t

A: As two questions are given , I will solve only the first one. Given : f(t)=3+e4t-te-2t+e5tcos3t+6…

Q: S T6 dar = tan-i +C 1 –1 16+z2 4 True False

A:

Q: solve the following Second order O.D.E d²y + 5y = -180x²e5x əx²

A:

Q: If y = u³ - 2u + 1, where u = 2√x, find at x = 4 -23 23 33 none of the above dy when x =

A:

Q: Q: Find tte value of z if e = 1+3 i Me

A: Solution:To find the value of k

Q: (d) ſhxdx jnxdx (е) [xsin? 2xdxх (1) f(5-t)*dt

A:

Q: a. Find 9 of the following. dx dy 2. y = (V4x – 3x)' 3. у%3D (4х — 7)11 (2x + 5)15 4. y = xVx(x? –…

A:

Q: r(t) = 4 cos(7t)i+4sin(7t)j+3tk

A:

Q: 1 What is h(z) dz? 2ri C4

A: In this question, we evaluate the complex integral by using Cauchy integral formmula.

Q: for the -j 3 O de terminant 2-j3 3 2 i-s 1

A: det3j2-3j3-3j-120-j1-j=3jdet-12-j1-j-2-3jdet-3j201-j+3·det-3j-10-j=3j-1+3j-2-3j-3-3j+3-3=-3-6j

Q: S D- If DW = 3x- 13 and DN = 2x + 8, find the value represented by x. %3D O 21 O 19 O 5 O 37

A:

Q: dy =ky, where k is constant and Yy=8 when =0, Also suppose that y=6 when 1=3, What is the dr %3D…

A: First isolate y with dy and then Integrate both the sides and the substitute the value given for y…

Q: ye'xdx (4 + e?x)dy

A:

Q: Find he value of ds/du at u = 2 if s t2 + 5t and t = (u? + 2u)

A: ds/du=9/2

Q: Find f f'Lx) = ZR? +aX-S and %3D to FlO)=4.

A:

Q: Suppose V - Geom(p) with p = 0.16 and that W = 2V. Find P(W > 8), giving your answer correct to two…

A: Solution .

Q: (a) Find where x² + 3xy + y² = 3 at (√3,0). da

A: topic- implicit differentiation

Q: dy 16x 9. If r? + y² = 8 then show that dr?

A: