Find f + g, fg, go f, and f o g where f(x) 1 and g(x) = sin 3x – Vx + 1 -

Q: Find  (f −1)'(a). f(x) = 3x3 + 3 sin x + 3 cos x,    a = 3

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Q: Find the general solution of f′(x) = −2x sin x2 .

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Q: Given g(x) = ln[(x^1/3 + sinx - 3tanx)/3x^4 - x^1/2], calculate g'(x)

A: Given equation is , gx=lnx13+sinx-3tanx3x4-x12 Let's find g'(x) Formulae we are using here,…

Q: sin x dx 4 3 Show that -

A: The integration can be written as;

Q: Find the general solution of f' (x) = -2x sin x2.

A: We have given the differential equation f'(x)=-2x sin x2. To find its general solution, integrate…

Q: 111. f (x) = sin 8x, (, 0)

A: We have the function f(x)=sin 8x In the point, the x coordinate is missing. To find the value of x,…

Q: Q: Find fo 1- y = tan/2/2x + 7 (x² +x)(x² -x+1) 2- y = x*

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Q: Find f' (x) for 8 sin(x) f(x) = -; 7x2 – 8 sin(x) s'(x) = |

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Q: COS X lim X0 ex

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Q: Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?

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Q: 2x + 2 Evaluate : sin :Ssi". dx. 4x² + 8x + 13,

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Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: .4 -1 sec J2 Evaluate x dx

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Q: f(x csc² 2x - x cos 2x)dx

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Q: Find f cos³x sin³x dx.

A: Given that: ∫cos3x.sin3x.dx

Q: 1. f(x) = 4x³ · cos x

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Q: 4 tan(x) sec2(x) dx = Select one: а. - 1 2 b. 1 С. 1 d. 1

A: Solve integration

Q: Find (f-1)'(a). f(x) = 2x3 + 5 sin x + 3 cos x, a = 3 %3D (F-1)'(a) = %3D

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Q: = (a) Evaluate S cosx sinx V1 – sin4x dx. -

A: Given∫cosxsinx1-sin4xdx

Q: tan ax x→0 sin bx f) lim ; a±0, b± 0

A: Given limit is : limx→0tanaxsinbx To find the value of the given limit.

Q: sin x dx V2-cos² x

A: Given : ∫(sin x/√2 - cos2 x) dx     ....(1)   Let cos x = t   Differentiating both sides w.r.t. x -…

Q: If f(x) = 7 sin(8a)sin-(x), f'(x) -

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Q: Find a function F(x) satisfying F'(x) = sin(6x).

A: Solution  Let consider differential  F'(x)  of function F(x)  so F(x)=∫F'(x)…

Q: (B) Evaluate f tan (7x +1) sec³(7x+1) dx.

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Q: f(x) = sin 23x %3D

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Q: f(x)= sin (x² +2x)

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Q: sin(x) is The solution for lim 1- cos(x) O 1 O DNE

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Q: dx sin-1x +c using method V1 – x2

A: Given:

Q: 2x + a + 1 if – 1< x < 0 Let f (x) = { x*sin (if 0<xs1 x*sin if 0 ) <x< 1

A: Given that f(x)=2x+a+1-1≤x≤0x4sin1x0&lt;x≤1 It is true that the function is continuous at [-1,0) and…

Q: (x²-2 (a) f(x) = 4, (sin 2x x + 2 (b) f (x) = { 1, x-2 at x = 2. at x = 0. X = 2 x = 0

A: A function is continuous at any point x=a if it satisfies the below condition. LHL=RHL=fa LHL is the…

Q: sin 2x J-1 x* +x* – x² +2

A: Here we have to find the integration: ∫−11sin2xx8+x4−x2+2dx

Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

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Q: f(x) = (sin 3x)*² %3D

A: The given function is as follows. Rewrite the given equation as follows.

Q: Find (f-1)'(a). f(x) = tan-(x) + 6x², a = 0 (f-1)(a) =

A: To find the derivative of inverse functions

Q: -r°(1-cos2x) 1- dx 2

A: 1). To evaluate the integral: ∫π01-cos2x2dx Solution: Evaluating the given integral.…

Q: 3x2 lim x→0 cos(2x) – 1

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Q: Find f'(x) if f(x) = e3X sin 2x

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Q: sin z coS T Q1-Solve by hospital rule lim

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Q: 19-f(t)=t-sin 2t; 20-f(t)=e" cos 2t.

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Q: 3. Find Df. 1 (a) f(x) = tan x (b) f(x) = 1- | sinx|

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Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = sin2 (x - 3y)

A: Given: fx,y=sin2x-3y  To find: ∂f∂x,∂f∂y

Q: Find a fixed point of x=g(x)=}+}sin(3x). ||

A: Given that                      x=g(x)=12+14sin3x To find a fixed point of the above equation we…

Q: Find y' at the point (4, 4) where x sin(x² – y²) + 13 = x² – 3. -

A: y = f(x) g(x) Then y' = f'(x) g(x) + f(x) g'(x).

Q: cos2x – sin2x cos2x F(x) +C. What is F(M)? For dx%3D cosx – sinx 3

A: A detailed solution is given below

Q: f(x) = 8x + 6x – sin(x), 0) =

A: Derivative: f(x)=8x5+6x-sinxWe know ddx(xn)=n.xn-1ddx(sinx)=cosx

Q: f(x) = x in the %3D sin 2x + ...

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Q: Find f(x). f(x) = V ?(4x) 10x-sin %3D

A: To find the derivative of the given function we use chain rule of the differentiation and some basic…