ve that Limit n + cos² . 2n cos + cos²P. p + r + cos?P. +...... 2n 2n f=1 4r

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: 3n + cos² . + 2n Prove that Limit + cos²P 2n cos²P p + r + cos?P 2 2n ...... 4r f= 1

A:

Q: Evaluate: S (In(2æ – 1) – (5) + 25 ) dx - Limits: [1, 6] Using Trapezoidal, n = 30

A:

Q: The area of the region inside r = 2+ cos 0 and outside r= 4- 3 cos 0 is given by T(2 + cos 0)? – (4…

A: We will find out the required area of the bounded region.

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

A:

Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: Find the limits in Exercise

A: We know that, limx→∞sinxx=0            ⋯⋯1limx→∞ax=0            ⋯⋯2      for any constant a

Q: (a) Show that z" + z=" = 2 cosn0. (b) Hence show that 32 cos5 0 = A cos 50 + B cos 30 + C cos 0…

A: Given:- Let z= cosθ+ i sinθ

Q: Solve 2 cos (t) - con(t) – 3 = 0 for all solutions. where ke Z

A: solution of the eqauation

Q: Let C be the shortest path that connects n to ni and I = S. (sinhz + 1)dz. Then Ι-1-cosh π+ π(-1)…

A: For the first question . Option first is correct answer . Thankyou !

Q: To show that rπ/2 sin" x cos" x dx: (m - 1) (m- 3) ... × (n – 1) (n - 3)... (m + n) (m + n - 2) (m +…

A:

Q: "ind no E N such that for all n > no sin(n + n² cos(n²)) n3 – 5n4 – 20 -

A: Find n0

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: 9. Let r = 3 sin tî + 3 cos tj + 4tk. Calculate N

A: Given r(t) To find N(t)------ unit tangent vector

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

A:

Q: Suppose m and n are constants and m #n. Evaluatesin (mx) cos(nx) dx' cos(m− n)x- = cos(m+n)x] + C 1…

A: Solution is here

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: In A XYZ, ZZ is a right angle and mZX = 53°. Which statement is true O cos 53* YZ %3D XY XZ O tan…

A: From the given figure representative diagram is shown below:   With respect to ∠53°.…

Q: du azu Find the solution to the equation = k at ax2 satisfying the conditions 1 - ax 0 at x = 0 for…

A:

Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: Which of the following is true? O Scos(3x)cos(4x)dx= [ r cos(x) + cos(7x) dx B Jsin(3x)cos(4x)dx= […

A: Option D

Q: Which of the following is true? @ - Scot*(x)csc°(x)dx = csc (x) 2csc7(x) , csc°(x) + C 9. 5 7 B…

A: integration if it helps, do like

Q: O Consider d = - CoSk; yeo) =0,iylo) Reduce he abore initial vaeue problem To be roltera entegral…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve 2cos? (x) +3 cos (x)+1=0 for all solutíons osx<2 TT

A: Given 2cos2x+3cosx+1=00≤x≤2π

Q: The value of the integral . rcos ydydr is cos 8 cos 4 b. - cos 8+ cos 4 2 1 c. cos 8 – cos 4 + Cos 8…

A: SOLUTION-

Q: Which of the following is true? ® Ssin(3x)cos(4x)ax =S sih(7x)= sin(x) A 2 ® Jsin(4x)cos(3x)ax = […

A:

Q: Which of the following is true? @ Jcos(3x)cos(4x)dx= [ cos(x) + cos(7x) 2 BAll of the above ©…

A:

Q: The value of the integral (s cos (r) dr is S COS Select one: O s(cos(2) – cos(0)) -

A:

Q: The area of the region inside r = 2+ cos 0 and outside r = 4 – 3 cos 0 is given by | ((2+ cos 0)² –…

A:

Q: 3x)=てメ+cosス そし-て)- -4-cosいて) そしね)、ずした) ):-Smいて)=20348 Kntl = Kn - ぐし) 0.9651+2.0 348 32 Satisfied…

A:

Q: 2 If s Sinants COs ant 3 an= ০ । A. limitdoes not exist 2.

A: Series and sequences

Q: Which of the following is true? A Jcos(3x)cos(4x)ax = [ cos(x) + cos(7x), 2 ® Jsin(3x)sin(4x)dx = […

A:

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

A:

Q: (B)JE w = x*+y+z° and x = PSin ø cos@ »y=pSing Sino and z- Pcoseo prove that -2P Cos 2Ø and' %3D

A: Given  w=x2+y2-z2x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ

Q: 1 Find the L s(s²+1) O 1-cos x O 1+sin x O 1-sin x O 1-cos x

A:

Q: Prove thet (1+ cose -isine)" +(l+ Cos e+isine)" = 2""cos (em). %3D Co."(을) COS

A:

Q: Please see the attached problem. Thanks!

A: Given:

Q: S-) Find the gereral solufon of Sin'x y"- (2sinx.cos x)g'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Given differential equation is sin2xy"-2sinxcosxy'+cos2x+1y=sin3x Here, qx=sin3x Given that y1=sinx…

Q: Which of the following is true? @ Ssin*(x)cos³(x)dx = - cos°(x) , cos®(x) cos(x) cos °(x) 6 4 10 ©…

A: answer of A:    Answer of B:

Q: • 8 If In = 7/2 e*cos" x dx, where n 2 2, prove that: %3D (a) In = 1-n[" /2 e-* sin x. cos"-1 x dx…

A:

Q: Fand ar a of functrons COSX n

A:

Q: and p(n) iF IF Fon) = 4 sec t dz.

A:

Q: 1 And the radios of Co for the pover Serie for the Power Serie vergence 00 xh (2"+1) (n?+1)

A:

Q: Let C be the shortest path that connects a to ni and I = ſ, (sinhz + 1)dz. Then |=-1-cosh n+ n(i-1)…

A: First option is correct.

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

A:

Q: Find all Solotioms Cin radins) to the eguotion 2 Sin X+V3= o

A:

Q: Q2-Prove that = va* – x² ify= ()sin () + () va² - x* = va² – x* if y = (;")sin*+ (4) + () Va² - x²

A:

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

A: Solution-