9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 + .... ..... den de, d02 de =1. de where %3D ..... de

Q: 9 NO ION If g(x) = [ cos t dt, find g '(x). %3D x10 -sin (x) -10x cos (x) COS 1 cos (x°) %3 10x9 cos…

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Q: 9 If f(0) = cos 0, ·cos 02· cos 03 ... cos 0n .... .·. f' (0) f (e) Show, {tan 01 + tan 02 + tan 03…

A: Given that we have to prove where

Q: 18. Evaluate ſe3 cos 2x sin 2x dx 1,3 cos 2x + C c.e3cos 2x + C B. -e3 cos 2x + C e3 cos 2x D. 6 sin…

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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: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: 2 lim In (cos x)e

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Q: 4. If y3 +x³ = sin y + sin x find. dx 3y²-cosy А. cos x-3x2 3y2-cos y В. - cos x-3x2 cos x-3x2 C.…

A: Given: y3+x3=siny+sinx To find: dydx=?

Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

A: We have to solve the given indefinite integral

Q: -3t 10. s = cj e" + c2 e" cos 51 + cz e" sin 51 + 123 O Sm + 5 Su + 17 s - 123 s = 100 O Sm + 17 Su…

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Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

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Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: - / sin 8x cos 5x dx = 1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x -…

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Q: Find the critical points of f (x) = 2 cos 3x + 3 cos 2x in [0, 2π]. Check your answer against a…

A: Given: f(x)=2 cos(3x)+3 cos(2x), 0, 2π

Q: 19. Evaluate: S A. VT- x² + arcsin x + C C. – VT- x² + 3arc cos x + C B. – VI- x2 +3 arcsin x + C D.…

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Q: 9 If f(0) = cos 0 · cos 02 cos 03 ....... cos 0n %3D f'() + tan 0,}=- f (8)] Show, {tan 0, + tan 02…

A: Introduction :

Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

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Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: 8)find dy/dt for y=cos^2(3#t-1) # is actually pie or 3.14 etc I just don’t have the symbol on my…

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Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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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: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

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Q: 4) f(x)=- - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 cos(3x) +... 12

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Q: - cos(x) - 1, choose all values of c in the interval (, 5 For f(x) guaranteed to exist by Rolle's…

A: For fx=-cosx-1, choose all the values of c in the interval π2,5π2guaranteed to exist by Rolls's…

Q: 4) u = x² sin=1 x 5) Ø = tan¬1 3 0 6) y = In(7 – 3x)

A: This question is taken from the derivative in which we have to find the derivatives of the given…

Q: In(x) limx→0* 0 e = 0 cos(re-x)+2

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Q: 4) f(x)= cos x COS X %3D (5) f(x)=xsinx -1+ Cos nx

A: Since you post more than one question. As per our guideline we can solve only first question for…

Q: Find L{(t – 1) (2 – 5 sin 3t)} . O 2 5s 30s - 82+9 (s2 -9)² 2 15 15 - - s2 (s² –9) $(s2-9) 15 15 2…

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Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

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Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)f () <0. f(x) has a root in [0]. If we use…

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Q: (2 2.) If f(x) = 2x 1 and p(x) cos (x). Find x, for 0≤x≤ 2π, if (f op)(x) = -2

A: Hi! Thank you for your question.As per guidelines we can solve one question at a time in case of…

Q: Which of the following is true? J sin(3x)sin(4x)dx = cos(x) – cos(7x) dx 2 ® Jsin(3x)cos(4x)dx = […

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Q: 55. f(x) = x² + cos ¹x on [-1, 1]

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Q: 1) / sen(x) 4+ cos²(x) I 1+4x² 2) [√5/2 S² 3) 0 4) 1 x² - 2x + 2 dx √ √2/2 are 0 X dr √2/2 arccos(x)…

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

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Q: Find L {(2 – t) (5 cos 3t – 1)}. 1 g3 10 + s2 +9 - - s2 s(s²+9) O 1 s3 10 + s2 -9 2 - - 8(s2 –9)…

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Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒf () < 0. f(x) has a root in [0]. If we use…

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Q: EX/ If f (x)= + COS2X CoS X is Pcx) Continlacaus at x=? %3D

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Q: S₂ 10 x 4x²8x +9 in14 (x-1)² +51 + √5 tan¹ (²²) + C Option 1 In 14 (x-1)² +51 + √5 tan¹ (2x = ²2) +…

A: SOLUTION-

Q: Г(x3 + 2х — 1) cos 4x dx A .3 13 x (3x² 13 sin 4x + 4 |cos 4x + C + - 4 32 16 128 B (x³ (3x² 13 |cos…

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Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: A Jsin(3x)cos(4x)dx = [ sin(7x) – sin(x). A dx 2 * cos(x) – cos(7x) ® Ssin(3x)sin(4x)dx= [co c) All…

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Q: Find L{(t- 2) (3 cos 5t + 1)}. COS 3(s2-25) (s²+25)? 30 | s2 s2 +25 6. 3 g3 s2 s2 +25 s(s² +25) 6s…

A: Find the Laplace transform of  L{(t-2)(3cos5t+1)}

Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: 9 If f(0) = cos 0 c • cos 02· cos 03. ... cos On f'(0) Show, {tan 01 + tan 02 + tan 03 + ....+ tan…

A: We have fθ=cosθ1·cosθ2·cosθ3....cosθn                 ....(1) Now, we have a formula…

Q: In2| 4+ tan-'cos- dx 2 sin ( 1+cos | 4+ tan-'cos- 2sin- · In²| 4+ tan-'cos- dx 2 (A 1+cos- 4+…

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Q: 5.S Vsin 2x . cos2 x dx

A: Integration is a process of adding up infinitesimally small pieces of an area. There are mainly 2…