19. f(x) = sin²: x cos 2x, 0

Q: 2. a) Find a formula for f-1 for the function y =f(x) = (x – 2)2 , x< 2 b) Evaluate the expression…

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Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

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Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: Prove 3sin x-45 in ³x = Sin (3x)

A: To prove that,3 sinx-4 sin3x=sin3x

Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = cos 2x

A: Given  f(x) = sin2x, g(x) = cos2x and h(x) = cos2x Then, we have to determine h(x) is in span(f(x),…

Q: sec? r da = F(x)

A: Given- ∫0π4sec2xdx=Fxab To find- The value of Fx Identity Used- ∫sec2xdx=tanx

Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: If f(x)- 3 cos 4x- - {).₁ 0 -3 -12 4 find f'

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Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: ifferentate: f(x) = COSX 1+sin x Apply the quotient ru

A: Topic:- application of derivatives

Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: 7. Find the second derivative given g(x) = sin x² A. 2 (cos x² - x sin x²) C. 2x cos x² 9 "(x) - 4 x…

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Q: 1 sin(x) (D²+1)³

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Q: 27: let f(x) = tan(x)+ sec(x) find f"(x)

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: Let f(x) = sin(4g(x)). Evaluate f'(x).

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Q: Find ao of the function f(x) 1-Cosx f(x) =

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: which is f-1 (x)? f(x)= 1/5x + 3/5

A: Given, fx=15x+35 We have to find f-1x.

Q: 1/2 105. Show that f (sin 0) de = f (u)- 1-и2 du.

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Q: Find the analystic function f(z)u+iv if u=a(1+cos0)

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Q: Find f"(7) given f(x) =- sin(z – 3x) our Answer:

A: Please see the below picture for detailed solution.

Q: J₁/₂ ( x ) = 2 TX .sin x

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Q: f(x) = cos x + 3, [0, 27], midpoint

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Q: . Express the function F(x) = 1 + sin x 1+ sin² x in the form (fog)(x).

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Q: What are the maximum and minimum values of f(x) = x + 2 cos x on the [0, π] interval

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Q: Vリ What is F'(;) 4 ? 16 π 4 π ミ|N

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Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

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Q: (v sin' 2) dn sin ædy

A: This is a question of exactness, non homogeneous differential equation.