86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

Q: Evaluate fSS, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the triple integration. For finding the solution first we will find the limits…

Q: If y= In(4 tan (4x) ), then y' tan(4x) = Select one: 04/(1+x² ) O None O 4/(1 + 16 x² ) 01/(1+ x² )…

A:

Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the integration over the region using the triple integral. First we will find…

Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos²…

A: Given: In=∫0π2x cosnx dx

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

A:

Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: Q- het m = 10-81 +3. compute the Suron E Sin (mntt) cos (m +2) (m+1)"+ COS n+1 n=1

A: The sequence of partial sums is very important in evaluating the sum of an infinite series. The…

Q: Evaluate the Integral 3sin2ß) 4 cos2ß dß. A 30 - (4 – 3sin2f) 5 + C (4- 3cos28) 5+ C B 30 -(4-…

A:

Q: 6.13 Show that t: = B,/[s//E=, (x;- %3D VI- r in (6.20). |

A:

Q: 3. Solve the following IBVP: Ut = Uzz + sin(37x), 00, u(0, t) = u(1, t) = 0, t> 0, u(x, 0) =…

A: Solution

Q: dy Find , if y = ein3x O None O cos3x. esin3x O 3cos3x. esin3x O 3cos3x. eCos3x

A:

Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

A:

Q: cos(3rk) In k 5k k 1

A:

Q: 21. Let h(x) = tan(5x + 6). Then %3D h'(2) is and h"(2) is

A: 21) The given function is: h(x)=tan(5x+6) To find h'(2) and h''(2)

Q: 1) VERIFY THE POWER REDUCING FORMULA, cos"x : cos 2x+1 HOLDS TRUE FOR 2 x = - AND x =

A: To verify:   cos2x=cos2x+12, for x=π3 and x=π2   NOTE: As per our answering guidelines, we can only…

Q: 6. Use a substitution to find S (x* + 1)" z³dx.

A: Here we use substitution we find∫x4+111x3dxHere we substitute x4+1=du…

Q: Let gt): csc (U) for Oct C! and CSC 2- 13/2- 2 How do I find fogle)

A:

Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: 1. Show that sinz is unbounded on C and lyl <|sinz] <ebl z=x+yi € C. for

A: Given:         We have to show that sinz is unbounded in ℂ and y≤sinz≤ey   for z=x+yi ∈ℂ Function…

Q: 4. Let z1 = 24(cos(75°) + i•sin(75°)) and z2 = 2(cos(15°) + i • sin(15°) ). Compute the %3D %3D…

A: SOLUTION-

Q: 28- For What Values of a anel k is a X <-1 ー<くく -2 Cx) = ax-b 3 Continuons at every X ?

A:

Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in E the first octant.

A:

Q: Suppose that cos 8 = 5/13 and 3T/2 < 0 < 2n. (a) Compute sin 0. (b) Compute cos 20 Hint: cos 20 =…

A: ANSWER :

Q: 3. Verify that u = e cos x is a solution of + 8² = 0

A:

Q: Show that (cos x + isin x)n= cos nx + isin nx whenever n is a positive integer. (Here i is the…

A: We can prove given result by mathematical induction: Define a statement p(n).  Show that p(n) is…

Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

A:

Q: If y= In( 3 tan (3x) ) , then y' tan (3x) = Select one: O 1/(1+x²) O 3/(1+9x²) O 3/(1+x³) O None O…

A: We are given that y=ln3 tan-13x. Now, we need to find y'. So,              ln3arctan3x'…

Q: Compute L{2et – 3 cos(7t) + t³}. а.

A:

Q: Express as a product.cos 5t + cos 6t

A: Given : cos 5t + cos 6t

Q: Show that in (5.2) the average values of sin mr sin nx and of cos mI cOs na, m+ n, are zero (over a…

A: Given problem is :

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: dq + q = 4 cos 2t dt

A: Given that, dqdt+q=4cos2t On comparing with general equation dydx+Py=Q ⇒P=1, Q=4cos2t, dx=dt…

Q: 18. Evaluate fe³x cos 8x dx e3x a. [8sin 8x 3 cos 8x] + C 3x b. [8sin 8x + 3 cos 8x] + C 73 C. d.…

A:

Q: C 3y° cos xydydx = O 3(1-Cos3) 5(1-cos3) cos3-1 O 5(1-Cos3)

A:

Q: Which of the following is a cubed root of (-/3 - 9? (A) 21°[cos(8z9) + i sin(8z9)] (B) 21[cos(7x/9)…

A:

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

A:

Q: If y= In( 8 tan-1(8x) ) , then y' tan-1(8x) = Select one: O 8/(1+ 64 x² ) O 1/(1+ x² ) O None O…

A:

Q: 2 7 4 is S cos' xsin xdx 비

A: See the details solution in below

Q: -) {in(6n) 2 n=2 =) an = In(6n³ – 4) – ) {cos(nt)}0 n=0

A: e) an=ln6n3-4-ln3n3+5n2-7n+8 determine if the series is convergent or divergent? if convergent find…

Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

A: Given,

Q: 3. Compute : exp(sin (ez).

A: simplification of complex term problem....

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: Q6:- Prove that: y" = 0 if (cos y3csc COS

A: To prove : y'' =0

Q: 40. Show that cos(30) = 4 cos e - 3 cos e for all 0. [Hint: cos(30) = cos(20 + 0).]

A:

Q: 2. Sketch 0 in standard position if cose = 8. and deter %3D

A: Given that: cosθ=-817

Q: (d) Show that there is some x with 0 < x < 2 such that x2 + cos(ax) = 4. %3D

A: Solution-