Which of the followings are true? I. D1000 re (2 - 1000)e IL D2021 cos(5a) = -52021 sin(5a) III. D20213 32021 e3z IV. D2000 1 7ェ 2 -2000!.72000 (7x –- 2)2000 O a.l, II, II, IV O b. 1,II O c. II, II O d. I, II, III O e. I, IlI, IV

Q: Find 7'(t), given ř(t) = ( – 4cos( – 5t), 3 sin( – 5t), e*). - - F (t) =

A: Solve the following

Q: (iii) 1 dø -sin²Ø Hint: may start with de (T(1/4)} /2 Vcose to obtain the result

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Q: 20. Which of the following statements are FALSE? dy 2л -5 I If y = In (7 - 5x), then de 7 - 5x 3e3x…

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Q: Transform F(s) (giving you cos 5t + t³

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Q: Q1\ Differentiate the following (choose two only) 1)z = sin (3x + 1) 2)f (x) = 3cot-12t 3)y = e 8*…

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Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

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Q: dy If y = x³ cos π, what is ? O 3r² - sin 7 -3x² sin T O 3x² cos T COS O-³ sin + 3x² cсos π

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Q: Evaluate the following integral. 3 4 4 cos '3x xp. sin 3x 1 18 4 4 cos '3x dx = V1- sin 3x 18 (Type…

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Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: The integral A B C D S³ x dx x² + √√√x²-1-1 sec²0 de 1+tano sine de 1 + cose sece tane de sece - 1…

A: We have to solve above integral

Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

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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: Evaluate: e* cos (7e*) cos (4e*) dx - sin (3e*) + –sin (11e*)+C A 22 B - sin (3e*) – –sin (11e*) +C…

A: Evaluation of the Integral

Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

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Q: Q2/provethate Cos17 +SinI7 cos17-Sın17 %3Dtun62

A: We have to prove that                               cos17°+sin17°cos17°-sin17°=tan62°

Q: Q25: A = e-2x – 3x5,B = 2Vx, C = sin³ 3x + 1 find A"" + B" - C'. (а) —8е-2х --sin 3x sin 6x – 180x?…

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Q: The sin(5x + 2x) dx cos5xcos 2x is equal to 2 In(sec 5x) + 5In(sec2x) +C А. 10 In(sec 5x) +…

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Q: p) S 64 cos4 2x dx A) 24 x + 8 sin 4x + sin 8x + C B) 64 x + 2 sin 4x + 4 sin 8x + C C) 2 sin 2x + 8…

A: Hence option (A) is correct.

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: What is the particular solution of (Dª + 4D² – 1)y = 44sin3x O a. cos3x O b. cos2x O c. sin3x O d.…

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Q: If sin x = siny = a and cosx = cosy = b, then cos(x-y) is Select one: O a. z2 + a² O b. 2b + 2a O C.…

A: Given  sin x = sin y = acos x = cos y = b Use cos (x-y) formula cos(x-y)=cosx cos y + sinx sinysin…

Q: dy Find if y = 5x² sin4x dr' O None -20x? cos4x – 10xsin4x 20x? cos4x + 10xsin4x O 10x? cos4x +…

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Q: Find: L [sin 2 5t ]. 0-co 5 Cos 10t) s² + 25 O A.) B.) 1 5 s² +25 2s 2(s +100) C.) D.)

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Q: Evaluate: / s r cos 0+r sin 0+5 (r cos 0) r dz dr d0 O 75¤/4 Ο 35π/4 О 65л/4 O 65x/3

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Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

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: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

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: Q1) Choose the correct answer of the following: exdx 1) is equal 1+e2x a) tan-lex + c b) In(1 + e2x)…

A: 1) a) tan-1ex+c 2) d) None of them 3) c) 1+x2 +c 4) c) 1 5) b) f-1(x) = 2x-2

Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: Зл ,2n) then tg 2 1 If α te( V1- cos“(a – n) + a)+ = 0. 3n – 2a sin(5n + a) 1- sin 2

A: We have to prove the trigonometric equation.

Q: ,Insec 2 (sin2y) dy Which of the following is one of the correct steps to evaluate the sec2y (A In…

A: topic - integration

Q: Find dr/dθ in sin (rθ) = 1/2

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Q: dy Find , if Y = (1+ cosx)sinx dæ cos3x + cos³x – sin²x O cosx + cosx – sin³x cos2x + cos²x – sin?x…

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Q: Which option equals Sx sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x…

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Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) b) y = sin(20) - 2…

A: Differentiate the following  a) y=-cos2x b) y=sin2θ-2cos2θ c) fθ=-π2sin2θ-π

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: Q12) If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( -,6 )?

A: Given ,fa,b,c=Cos abSin b+CPut 12,π3,6i.ea=12 ; b=π3 ; C=6

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

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Q: 0, o° s 0 < 360°, given the follo Cos e = and 0 in QIII 2.

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Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: S(32+2*)sin(z)dz 3z +

A: In this question we have to solve Integration.

Q: If f(x) = 12sin(green wave), then the red wave isi %3D 20 |-3T/2 -TT T/2 TT 3h/2 2n |-10 IF f(X)=12…

A: Red wave satisfies the point -π2,0,3π2,0  a) Given,   6sinx+π+6 Put x=-π2…

Q: One of the correct steps to evaluate A sin²20d0 [² B cos 40d0 C) None Ⓒ//ww D do + sin²20d0 Ⓒ = [ √…

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Q: St² sin(2t*)dt A 1 (sin(2t*) – 2t*cos (2t*)) + C (sin(2t*) – 2t*cos (2t*)) + C 14 B D (sin(2t*) –…

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Q: Find :L [cos h 5t sin 2t] a.) (s²-25)(s²+ 4) [ल. 2s b.) (5-5)²+4 c.) 1. (5-5)²+4 (s+ 5)?+4 dl.)…

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Q: Which one of the following equals (x + y) dæ dy. T/4 OA p2(cos 0 + sin 0) dr dð Зя/4 - 7#/4 " […

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