cos2x – sin2x cos2x - dx=- + C• What is F(x)? For cosx – sinx 2 sinx - cos?x – cosx+ sin³x 3 3 (sinx – cosx) -3 O (cscx – secx)3 2 sinx +-ços'x+ cosX +

Q: Evaluate / 4 x cos(x)dx Ox sin(x) – 4 cos(x) + c 04 sin(x) + 4 x cos(x) + c 04 (x sin(x) + cos(x)) +…

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Q: limg-0 2x sinx 4-4cosx

A: We can find the limit as below, using L'Hospital rule.

Q: s+1) (a) L-1 4s2 +1 (b) L-1 s4 + s] (e) E{/ c{[e cos(r) dr.

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Q: sin (x) – cos²(x) Show that 1 F COS %3D CSC (x)

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Q: Sx-3) (sin (In x) + cos (In x)} dx equals

A: Here we have to evaluate I=∫(x-3)sin-1lnx+cos-1lnxdx

Q: integrate (cos (x)/(sin(X)-cos(x))

A: Integration is a technique of finding a function  the derivative of which, , is equal to a given…

Q: cos( 2 sin1 (X/17)) = Select one: O 2x ( 289 - x )o./ 289 O ( 2x - 289 )/289 None O 34 x/( 289 + x)…

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Q: If f(x) = sin x, show that f(x + h) – f(x) = sin x cos h – 1 sin h + cos X h h

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Q: sec“ x 8. dx 6 tan x – tan² x

A: One of the two main parts of calculus which are concerned with the study of integrals are opposed to…

Q: 9. Simplify sec² x - 1 sec² x

A: secx=1cosxI=sec2x-1sec2xsin2x+cos2x=1

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: EVALUATE Зд - 2 (c) dr x2-6x+ 8 EVALUATE sin-1x dx V1-x2 (d)

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Q: COS X lim x0x +3

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Q: If f(x) = sin?x, then f"(x) = %3D A 2cos2x B cos2x -sin2x D -4sin2x

A: Given, f(x) = sin2x For the given function , applying chain rule ,  First differentiate it as { xn ,…

Q: sin x = csc 2x cos x cos 3x sec 2x

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Q: Sx [x²cox dx U. V x² Sax - S(α (x²) [ cond) dx dx x² (sinx) - -S 2x Sinx dx U. V. x² sinx - [2x…

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Q: / (cos(x) + Ex dx 4 +

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Q: Evaluate / 4x cos(x)dx

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Q: cosx sec? x + cos x csc csc? x csc? x secx cos? x cos x cos x E f(x)dx _ 2 1. If f(x) 1 , then

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Q: 2tan(x) dx 1 – tan2(x)

A: Solution:Given     ∫2 tan x1-tan2 xdxFormula:tan x =sin x cos xcos 2x=cos2 x - sin2 xsin 2x =2 sin x…

Q: -1 sedx- cos(

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Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

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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: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: If f(x) = 6 sin(2x)sin-¹(x), f'(x) =

A: f(x)= 6 sin(2x) sin-1(x) f'(x)=?

Q: tan(x) – cos²(x) dx Evaluate: cos(x) A sec(x) -sin (х) +с B B sec(x) + sin(x) + C © sin(x) – sec(x)…

A: We can find the integration as below

Q: sin(v3t) (b) L-- [tan- )) (a) L dt

A: In this question, we use the properties of Laplace and inverse Laplace transform, find the Laplace…