sin?x If h (x) = | . (t² + 1) dt for –

Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: 7. h(x) = tanx- tan 8. h(x) = 3 sec-x

A: we have been given the equations to differentiate w.r.t x

Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

A:

Q: tan"x jun's de - | tan"-x dx (n 1) n- 1 tan x sec" r sec x dx (n 1) n- 1

A:

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

A:

Q: Evaluate cos x+ 2 cos x+1 dx sin x sin x - 3 cos x cost x 7. +x+c 2 cos x +x+c 3 cos X- cos x (sin x…

A:

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

A:

Q: lim x→0 (sin10(x)cos(8x))/x=?

A:

Q: 2 n- tan x sec"- 9. Show that for n > 2, п-2 sec" x dx + n - sec" 1 x dx п — 1 | 4 Use this to find…

A: You need to use reduction formula to integrate the function, such that: You need to use integration…

Q: b) (cosx+ Sinx)² - Cos x+sinx)(cosx-Sinac) tan 2x 2. c) 1-Cos-x - Sin2oc) Sin X - 2cos x

A:

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

A:

Q: sin- In2 4+ tan-'cos- dx 2 2 I+ cos2* 4+ tan-'cos- In2 4+ tan-'cos- dx 2 2sin- 2 A 1+ cos 4+ tan…

A: To evaluate: ∫sin x2 ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

A:

Q: e lim Secx-1 Sinx (-esux) 3}r® २5 ९६० 5x 2 lim ーD6 Sin5x of Sin4x. e lim メーD6 よ + tan 38

A:

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

A:

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

A:

Q: 1-sin(x) (1-Sinx)2 10. Find the equation of the line tangent to the graph of y = 3cos(x) at the…

A:

Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

A:

Q: cos x + sin² x + 1 dx cos² x (sin² x + 1)

A:

Q: sin xV1+ cos 2xdx 6. V1 - sin 2xdx 7. 8. cos' xdx 1+x+x? -dx x² + x3 9. I sin 2x 10. I + sin² x xp-

A: Note: As per company policy we are supposed to solve only one question, So kindly repost the other…

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: Find Critical Points and Extreme Values: f(θ) = 2 Sinθ + Cosθ        on [ -2π, 2π ]

A: Given         The critical point is where  f'θ=0              Here the interval is -2π,2π…

Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

A:

Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: 1. f(x)= xsin x 2. f(x) = x?cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) =

A:

Q: x+ cos x 4-lim X-0 \sin x cosx.

A: For the existing limit at the particular point, the Right-hand side limit should be equal to the…

Q: (x² +1)Z. tan-1(sin 2x) Q2/ B/Find dy if у 3 dx (x2 +4)3 . sin-32x

A:

Q: 1- COs x lim x→0 3x sin x

A: This question is based on limits.

Q: Example 2: find ỹ,y=sin-1 Vx.sec-1 (sin x) Example 1: find ỹ,y=tan-1(x². sin x) Example 3: prove…

A:

Q: 12. Find the first derivative of y = 2cos(2 + x*). A. -4x sin (2 + x2) B. 4x cos (2 + x*) C. x sin…

A: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

A:

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: F CSC'x + - cos2x -cos^x -sec'x

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: of y= sec(x*) . 4. Find 2xsec(x?)tan(x²) sec(2x) tan(2x) O sec(x³)tan(x²) 2sec(x)

A:

Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

A:

Q: 2 X (x-sinx)2 | 6x'sin² 2 3/2 - Evaluate: +3x dx. X, X-sinx

A:

Q: ∫ sin3 (x / 2) cos (x / 4) dx

A:

Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

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Q: (cos(2x) – sin(2x) cos(2x)) cos(x) – sin(x) For -dx%3D +C. What is F (x)?

A:

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3D cOS x 1+2y + cos x-sin x 1+ sin x 1+ 1+ cosx 8.…

A:

Q: 1+sin x+cosx 1+cos x (b) 1+sinx-cos X sin x

A:

Q: 3e" - 2 sec x tan x + cos x - 3 dx 1+x?

A: Given:

Q: 1+sin 2 x Find the derivative of f(x) 2 cos3 x

A:

Q: 1. lim sin x sin 2x x-0 1-cos x 3x+x+2 . lim X-4x3+8x+1

A: d) To evaluate                       limx→0 sin x sin 2x1- cos x                            =sin (0)…

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3| cos x 1+2y + cos x- sin x 1+ sin x 1+ 1+ coS x…

A: Introduction :

Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

A:

Q: Solve over the interval [0,2pi)

A:

Q: ∫(3 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

A:

Q: cos(2x)- sin(2x)cos(2x)) cos(x)- sin(x) dx = -F(x) + For C. What is F (x)? 3.

A: