I lim 81x In(x+n) n cos a dr

Q: Simplify 2sin(4x) cos(4x)

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Q: Evaluate 5⁰⁰ x dx. -∞ x sin 2x x²+3 0

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Q: 2 cos² x√4 tan x S tan² x dx

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Q: find cos 0 el - (1 + h) 43. lim 0-0e" - 0 - 1 44. lim

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Q: Evaluate 2 cos ( 3x – when x is 4

A: Given query is to find the value of the expression.

Q: ((주)' lim x (1- cos () COs X->- 00

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Q: Let f: X → Y and g : Y → Z be functions. (a) Show that if g of is one-to-one (or "injective"), then…

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Q: (15t-2 – 5t) cos (6t-1+t²)

A: using substitution method to find integration

Q: dx 1+x2 A In(1+x²) + c BIn(1+ x²) + c c tan-ix +c 1 x 2 D tan-x+ c IN

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Q: sin 2.r =? lim Vr3 + r² - x -1 2 112 112

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Q: Evaluate 2 (y + y cos x)dxdy -3

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Q: Cos(10+x)

A: Here , We will apply the formula of Cos ( A+B) Cos(A+B) = [CosA CosB - SinA SinB ]

Q: secx-secx COS x 2+anx sinx-secx

A: Given To simplify sec x -sec x.cos2 x2 tan x - sin x.sec x

Q: sin (an) - 3cos² (5n) √5 n

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Q: x2 %3D x2 + 1

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Q: e cos3t Find L

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Q: Evaluate COs 2 4 – x² dx

A: use the property of even function and odd function to evaluate the integral.

Q: (sinx –) limx- (3sin²x –sinx +1) 21 7 →- 6. 2

A: Answer is -2.

Q: Evaluate 3 L, cos¹ (2+1) dr. -1

A: l have given the answer in the next step. Hope you understand that

Q: sin(3x) – sin(3) cos(2x) lim Select one: O a. does not exist O b. 0 OC. O c. -6 O d. 6

A: we have to find the limit of the following

Q: -t 2 lim 8 cos t 2 T 2 16 16 2.

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Q: Q5: Show that S 2T Cos 30 5-4 cose 11 ㅠ 12

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Q: a sin(x) -dr. Jr (r² + 1)(x² + 16) R.

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Q: Find So Cosx (x² + 1)² - ex

A: We shall be using basics of residue calculus to evaluate this integral

Q: Lim 8X +4=4 Cos X +tam

A: To find the given limit

Q: (cos(3x+ 1))² lim 7+ 4x

A: our objective is to find the limit