Let f a continuous function in [0,1], an integral equivalent to π/2 f (cos(x)) sen (x) dx 0 after applying the variable change u=cos(x) is ? 1 O a) - - √² f(u) du 1 Ob) ff (u) du O c) O d) π/2 - [*/² ƒ (u) du f 0 π/2 [/2 ƒ (u) du 0

Q: sin x then

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Q: Let f(x) = 3 cos a - 2 tan a f'(x) = r() - C f'

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Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

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Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

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Q: Show that

A: ∫x f(x) dx=x F(x)-G(x)                                  F'(x)=f(x)G'(x)=F(x)

Q: Find f. f(0) = = f"(0) = sin(0) + cos(8), f(0) = 3, f'(0) = 2

A: f"θ=sinθ+cosθ Integrating both sides  ∫f" θdθ=∫sinθdθ+∫cosθdθ f'θ=-cosθ+sinθ+C..... (i)  Put θ=0…

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: Let f(1) = 8 sin z +5 cos z %3D f'(z) = %3D

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Q: Let F(x) –3 cos(ť²) dt. Use the Fundamental Theorem of Calculus to find F'(x). F'(z) =

A: Given: F(x)=∫x−1(−3cos(t2))dtF'(x)=ddx∫x−1(−3cos(t2))dt=?

Q: Let f(r) = cos(4r + 4). f'(x) =-4 sin(4r -4) f'(2) = | 0

A: Solve the given problem.

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

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Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Let Find f(x) = y = f(x) = 5x + 18 cos x. d f(x) =

A: Given query is to find the derivative at indicated point.

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: What is the domain of f(x)=cos-'(In(x))? Select one: O (0,1) O (0,0) O (0,e]

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Q: Let f(x) = tan (cos(2æ)) f'(x) = Preview

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Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

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: What is the total change of f(x), if f'(x) = cos(2.5x), over the interval [0, π ]? -1 -0.4 0.4 0.6

A: The derivative of f(x) is

Q: Let f(x) = 8 sin r + 3 cos r f'(x)- f(똥) =|

A: The given function is f(x)=8sinx+3cosxTo find f'(x) and f'5π6

Q: f(z) = cos(4r +5) %3D

A: we have to derivative  we know that  d(cos (ax+b) ) = -sin (ax+b) a                        = - a sin…

Q: Let f (x)  =  (tan−1(x))2. Find f '( 1/3).

A: