(3) Prove that πόληΣ one (= -10+1}], [cos² (π (n 1)! π(κ) = n 25η Σα where “π” within the sum stands for the constant π = 3.14159...

Q: 1) Solve the ODE below. a) x²y" - 3xy' = x²

A: According to Bartleby guidelines I have solved first, since this is not interrelated question,   For…

Q: Prove that n r=0 "C, sin rx.cos (n-r)x=2"-¹x sin nx. 1

A:

Q: a) L{te-3t cos 3t}

A:

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

A: Given,

Q: ). Show that V - u -ly- tan' u < V - u 1- if 0<u<v, < tan 1+v? 1+u 4 2< tan 4 25 3 and deduce that 3…

A:

Q: SP, (cose) cos no de Pn = B (n + 1, ¹), n€ N.

A:

Q: aluate ㅠ - π 2 cos² (9x) dx.

A: Remember :  cos(2x)=2cos2x-1⇒cos2x=1+cos(2x)2 we have to find  ∫-ππcos2(9x)dx

Q: QuestionTO cos( z+ Da sin(e-2+ In(z)) + C 4 Ob. -4 sin(e-z+ In(z)) + C Oc. --- sin(e-z+ In(z)) + C 4…

A: Given query is to evaluate the integral.

Q: If I, = e cos" zdr, where n > 2, Prove that i) I, =1-n e sin z cos"- rdr

A: Given,  In=∫0π2e-xcosnxdx solving by using Integration by parts, Formula of integration by parts,…

Q: Show that M8 Σrk k= pk cos(ak) = −1+ 1-2 2(r2-2r cos a+1)

A: Using summation of infinite series in geometric series Sum = first term /(1- common…

Q: de − 7 √(1-k² sin²0) 2F₁ ( ½ ‚ ½ ; 1;^²), \K[<1

A:

Q: $ S®- floor't. & сод

A:

Q: Z1 "(cos(0, r2 Z2 02) + isin(0, – 02)](z2 # 0). 85. Let z1 = ri(cos 0, + isin 01) and z2 = r2(cos 0,…

A: Given z1=r1cosθ1+isinθ1 and z2=r2cosθ2+isinθ2.

Q: Compute at 0 = 0. de [tan (20) + 04]

A: here we have to find the differentiation.

Q: 5. [10] Use DeMoivre's Theorem to expand [4(cos 60° +i sin 60°)]". Write your answer in a + bi form.…

A:

Q: Prove that "C, . (n-r) COS r=0 2ræ n = -n.2n-1.cos n T - n

A:

Q: 6. For positive integer n, prove the following (given that I(½) = √√): √π = (2n)! √T. 4nn! T(n +…

A:

Q: sin(6x) lim ? 2+0 sin(2x) Does not exist O 3

A: Given problem:-

Q: 6. f cos³x√sin xdx)

A: sin2x+cos2x=1∫xndx=xn+1n+1

Q: (a/3 d(cosx) =? 24 - sinx O A) V3/2 O B) 1/2 C) -1/2 O D) -1/3 E) T/3

A:

Q: (25) Let k and n be positive integers. Prove each of the following: sin (n2) dz = | cos (nx) dz = 7.…

A:

Q: Hello. I need to solve two functions on maple. The first is t*sin(t) and the second is…

A: As per the question we have to plot the following curves using Maple in the interval [-5, 5] t…

Q: Find the exact value of 1 - O sin(√2) O cos(√2) cos(2) O ln(1 + √2) O e ² 2 2! +4 8 6! + 16 8! 32…

A:

Q: Prove that there exists a value of x so that -1 COS T = cosx %3D ned to

A:

Q: Sæ³ cos(x*) dæ =

A: We solve it by u part method , ∫x3cosx4dx Let u = x4 Differentiate both side , we get   du = 4x3dx…

Q: e) Find all solutions of 1+ cos? x = 2cos² [0, 2.7). in the interval 5e.

A:

Q: Show that in the interval (0,1) COS TTX = ∞ TT n=1 n 4n²-11 -sin 2nπx

A:

Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: Prove that the inequality | cos(z)| 21- sin"(z) holds true for all z € R

A:

Q: T/2 TT/6 sin x 2 1.)Prove that

A:

Q: 2. L{sin² = nt} 7² a. S³+π²s π² b. 772 2s3-2π²s π² C. 772 2s3+2π²s π² d. S³-π²S

A:

Q: 1. Evaluate (3260)"]" × (-5+ j6) (cos(3 + j5)]1-/) Sin sin-

A: We have to find: sin-13∠60°3*×-5+j61jcos3+j51-j. We will find the interior parts first on different…

Q: Question (1): Find the equation of the straight line passing through the intersection of the lines…

A: Given: equation of lines are: x - 2y = 1 and x - 3y = 2  These are intersecting.   To find: the…

Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

A:

Q: 5- Prove the following (Answer two only): secA. secB.cscA.cscB a- cos*e – sin*o =cos²0 – sin²e c- =…

A: Answer 2 only.