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

Q: cos 2t dt 2.

A: Given:             ∫-π3π31-cos 2t2 dt Take the constant out: ∫a·fx dx=a·∫fx dx…

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 )…

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Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

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

A: Given limn→∝ 1ncos2pπ2π+cos2π2n+....+cos2pnπ2n=limn→∝1n ∑r=1ncos2prπ2ntaking n=1nthen takling…

Q: -1 Exercise 9: Evaluate cos V10, leaving your answer in terms of surds.

A: The expression is cos-110

Q: A-Show that S 1, L{cos at} s2+a²

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

Q: Compute the Jacobian of : O(r, 0) = (9r cos 0, 4r sin 0)

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Q: 1-[t2 cos at

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Q: Which of the following is equivalent to the definite integral 7/2 | (cos(72) + 7) dæ? 1 [,sin(7m/2)…

A: Definite integration

Q: A periodic signal is given by r(t) = 3 cos(t) + cos (5t 2n - 2 sin (8t + 3

A:

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

A: Find n0

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

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

Q: Q.3- Prove that: 2n 1 (cos =0 +i sin-) + 10 2cosne eino

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: evaluate the triple iterated integral.

A: Given: ∫0π4∫0π4∫0cos∅cosθ dρ dϕ dθ

Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

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Q: 7)Use Taylor theorem to estimate cos(0.23) with Jerror|< 10-2

A: Here we are to estimate cosx at x=0.23=23100 with error≤10-2,using Taylor theorem i.e, using Taylor…

Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

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

A: Given 2cos2x+3cosx+1=00≤x≤2π

Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

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

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…

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Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

Q: Solve for tt, 0≤t<2π0≤t<2π 10sin(t)cos(t)=4cos(t)10sin(t)cos(t)=4cos(t)

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Q: 1 with in Ql , find sin B = B If cos B B Cos 3- 2/2 6 3- 2/2 Cos B COS 22 3 B cos 3 + V3 3 + 3 Cos 6…

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

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

A:

Q: Q3/ Determine: (a) sin(t) .8(2t – 1) (b) (cos nt). 8(t- 1)dt 8(t –

A: As per our guidelines we supposed to solve the very first question if the multiple questions are…

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

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Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: 2. Find a closet rank-1 approximation in the f norm to A = cos 8 - sin e sin e cos 0

A: According to the given information it is required to find closet rank-1 approximation in the l2 norm…

Q: 1. Evaluate the integral 7/2 cos xesinx *dx

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Q: 1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

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Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: 3. Show f cos2n Ode 277 sin-n Ꮎ ᏧᎾ = 27 22n 11.1 n = 1, 2, 3,...

A: Using Cauchy integral formula.

Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: Fand ar a of functrons COSX n

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Q: Evaluate the integral. sin (3u + 7) du dv dw 0 00 2 O A. z cos 7 1 O B. 국COS 7 OC. 1? cos 7 1 O D. 1…

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Q: 4. Write u = -2 cos Tt – 3 sin at in the form u = Rcos(wot – 8).

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Q: Solve the eaation on the interval. 2sin Đ =3(cos o t D

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Q: 2n 1 (cos=0 0 +i sin e) + 10 2cosno eine

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

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Q: Find the values of z satisfying cos Az = 0 2

A: Result : General Solution of  cosx=0 is x=(2n+1)π2

Q: Find the exact values of sın 20 and cos 20 for cos e on the interval 0° S 8590° sin 20= 0.7744, cos…

A: Use the identity sin2θ+cos2θ=1 to evaluate the value of sin θ. sinθ=1-cos2θ=1-372=1-949=4049=2107

Q: Question 6 Compute the following integral: sin (8z) de 1 4 a) cos(8x) sin*(8x) + C 32 1 cos (8r) + C…

A: