f(x) = Cos (3x) as a 6th degree polynomial centered at x = 0. Hint use the following: P₂(x) = ƒ(0) + ƒ'(0)x + f" (0) x² + 2! f(0) x³ + 3! f(n)(0) n!

Q: Let f(x) = (sin(x))*. Find the value of (a) 1 (b) 2 (c) 2 (d) 2 (e) 0

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Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

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Q: x () - (-). y (1) J

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A: Given fx=-2x3-x-5f-1=-2Therefore, f-1-2=-1Differentiate with xf'(x)=-6x2-1f'-1=-7

Q: If the function f(x) is defined as f(x) = = (4-2√√x)² √x -,x>0 Then, what is the value of ƒ'(16) = ?

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Q: Find f. f(x) = 3 f'(x) = √√√x³ + ³√√x + 5ex + sec² x, f(0) = 8 4

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Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: 2 For the function f(x)=√x² +4, find f''(x). Then find f''(0) and f''(9).

A: Given query is to find indicated derivative.

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

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Q: F = If SF · dr = (5x − 3y²) dx + (x³y) dy, what is F?

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Q: If f(x) = cos(2x), then f"|

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Q: (2) GIVEN: f.R- R, Sx) = x²(3x– 1). Find f'(x) in factored form.

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Q: Given f(x) = x + 4, x < 0. Find (f-1)' (5) 10 1 2 | 29

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Q: f (x) = x5, x = 1/2

A: The function is given as fx=x5

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Q: Find an anti-derivative F(x) of f(x) = 7x³ – 6x² –- 1 satisfying that 7 F(1) = 4

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Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

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Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

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Q: 5 Find f such that f'(x) = - √x f(16) = 49.

A: f′(x)=5x,f(16)=49

Q: h(x) = In (a- 7) (r +3)

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Q: The 7th derivative of f(x) = 3x5 - 12x¹ + 7x³ − 11x² + √5 with respect to a is O 360T O none of the…

A: Topic = Derivative

Q: For f(z) = 2es'the value oflog(f(z)) is

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Q: Esc [3] Use a first derivative test with a well written conclusion to state the local min and max…

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Q: Find F(s). F(s) = L {tu(t = 3)}

A: detailed solution is given below