Exercises To Solve [No.5] Lim 5 9-5 dx -x²8x-15 D "Cosx dx Sin x+25inx+5 b

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

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

Q: lim Sinx (1-cosX) 2x2

A:

Q: X+1 dx (x- 1)(x² + x + 1)

A: The given integral is: I=∫x+1(x-1)(x2+x+1)dx

Q: S(csc x cot x + 9x°)dx Csc x + x° +c - sec x + x³ +c | CSc x + x9 - sin x + x³ +c sec x + r9 + c

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

A:

Q: 2 + tan? (t) Simplify -1 to a single trig function. sec2 (t) No quotients. 2 + tan? (t) sec2 (t)…

A: Use the trigonometry identities and simplify.

Q: sec² (8t) tan² (8t) dt 16 – tan² (8t)

A:

Q: sec2 () dx x3

A:

Q: (2sin x - 1) (csc x - 2) = 0

A: Given: (2sin x − 1) (cosec x − 2) = 0

Q: 3 Lim x40 Cosx (2 Cos²x - 1) Cosx -

A:

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5)| (3220° – sin 20 + jln5)*|

A:

Q: 4 sec 2x tan 2x dx (1+ sec 2x)²

A:

Q: Salve for x if Arc tan (1- x) + Arc tan (1 + x) = Arc tan

A: Our Aim is to solve for 'x' if tan-11-x+tan-11+x=tan-1x -(i)

Q: In(cos ax) limx-0 ? In(cos bx)

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Q: 36" -dx V6* +3

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Q: x+2 lim sin - x+6x+8 3 2.

A:

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 9. Simplify sec² x - 1 sec² x

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

Q: Solve using +00 S 0 residues x³ sin (3x) dx 2x² + 1)2 2X

A: Let f(z) be a complex valued function,  then ∫Cf(z)dz=2πi×∑R Where C is closed contour and ∑R is…

Q: sinx dx cos³x (1 – sec*x)3 A)를 (1-sectx)-4 +C B)를 In(1 sec*x)3 + C c)금 (1-sec+x)-2 + C D)름…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: (a) (b) So (arcsin x)² dx 0 L cosh² x dx 2

A:

Q: How to graph sin(x) + sin(2x)?

A: Given: The objective is to plot graph for the function sin(x)+sin(2x).

Q: 2х-п lim =? COSX 2

A: We can use differential calculus to find the solution. When we directly apply the limit we get an…

Q: sin3 x dx (③)글 4 () (0)

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Q: cos 2 arctan X - 1 √x+1 /x+1/

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Q: (5x+sin3(4x) + sin(4x³)) dx

A: use differentiation for finding the solution.

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: lim, 0 6 tan² (5x) 15x²

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Q: (c) tan(2x)

A:

Q: S(sec x tan x + 9x*)dx

A: The integral ∫secxtanx+9x8dx can be calculated as, ∫secxtanx+9x8dx =∫secxtanxdx+∫9x8dx…

Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…