7. Determine the solutions for sin x 1- cos x sec x x € [- 2₁1, 1] (Hint: simplify the equation first) in the interva

Q: b) S sin 2 x cos x dx

A:

Q: 1. Find the derivative 4 ln 2) ³ 3x³ sin(2x) 5x2+3

A:

Q: 4). Evoluate 2. (88e0 COS X cot x)dx 4

A: Definite integration

Q: is a root of the equation y2 + ycot x cos x - 1 = 0

A: Here we have to show that, y = sin x is a root of the equation y2 + ycot x cos x - 1 = 0

Q: find f'(x). Answer: f(x) - 5 sin x 1 + cos x

A: f(x)=5sinx1+cosxd dx(sinx)=cosxd dx(cosx)=-sinx d dx(ab)=b×d dx(a)-a×d dx(b)b2

Q: ] 1 1-x² dx = tan¹(x)

A:

Q: Determine a root of the equation sin x + 3 cos x – 2 = 0. Correct to four decimal places

A:

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

A: 5)  Let , I = lima→5 ∫a-4 dx-x2 - 8x - 15 Let , us simplify denominator first ,  -x2 - 8x - 15 = -x2…

Q: Differentiate the following functions. Simplify and factor your answer where possible. a) f(x) = e2x…

A:

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 1. f cos³ (tan x) sec² x dx

A:

Q: Show that the equation tan(x)=1−x has a real solution.

A: Using Newton raphson method.

Q: I. Eliminate the arbitrary constants -3x y= C, e sin2x + - 3x Cze cos 2x

A:

Q: Solve the equation sin(x) - cos(x) =1. from[0,1].

A:

Q: 2270 d) V3 cosx + sin x = 0 (-2x, 0]

A: First, we rewrite the given equation in a more familiar form. The given equation…

Q: 2. (a) Show that V3 cos x-sin x COS where 0<x<2r . 2 (b) Using the result in (a), solve the equation…

A:

Q: sin x (cos x + 4) dx 1+cos?x

A:

Q: dr = b (cos(O)dr + r sin(O)dO)

A: Given dr = bcosθ dr+rsinθ dθdr(1-bcosθ) = rsinθ dθdrr = sinθ dθ1-bcosθintegrate on both sides to get…

Q: Solve (tan x – V3) (2 sin x + 1) = 0 , where 0 < x < 2x .

A:

Q: 3) Solve S(4cos? x+4 sin? x)dx

A: Given:

Q: cos 0 = √√2 -|~

A: Let's find angle theta.