Let y = f(x). Begin by finding the derivative of f(x) = -x³ + 6x² - 3. 3 F'(x) = (x³ + 6x² − 3) d dx Therefore, the second derivative is f"(x) =

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A: The given function is

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A: Horizontal asymptotes of the rational function:Vertical asymptotes of the rational function: The…

Q: 4. Find the derivative of the following functions: a. y = x² sin x b. y = ex cos x 3 c. y = (x² + 1)…

A: *Note – As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly…

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A: Given that the expression

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Q: lim У-у-г уг -30+2 зу Уже

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Q: Evaluate the following: lim In(e+h)-in e

A: To evaluate the following limit.

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Q: Question 1 If you know that Q(x) is a quadratic function and that Q(8) = 7, Q(7) = 2 and Q(1) = 6…

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A: R'(x)= 0.03x2-0.08x+189

Q: Find the general indefinite integral. (Use C for the constant of integration.) [(cos x + x)dx…

A: The given integral .The aim is to find the solution to the integral and sketch its graph.

Q: Let Z₁ = 6(cos(72) 7π -54 Z1Z2 = Z1 = Z2 + i sin (77)) and Z₂ = X 9(cos(55) + i sin (57)). Find Z₁Z2…

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A: Given that the function are

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Q: 1. The general solution of the system [x' = y, y' is given by x(t) = C₁ cost + C₂ sint, y(t) = C₁…

A: x'= y..........(1)y'= -x.........(2)

Q: lim       sin(π+h)- sinπ                                      h→0     —------------…

A: Note:-Since your part a incomplete ,please repost part a again(b)

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A: The given equation is; 9cos(2t)=9cos2(t) -2, [0,2pi)

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Q: If f is continuous and f(x) dx = 12, find So f(2x) dx.

A: Given that To find

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Q: Find the Taylor polynomial of degree 3 of the function f(x) = arctan(9x) at a = 0. T3(x) = ||

A: f(x)=arctan(9x), a=0

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A: The mass of the Freshener a=42 gmIf opened in the air decreases to  4.2% per dayThis means the decay…

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Q: Stoite the Fundamental Theorem of Calculus?

A: we need to write down the fundamental theorem of calculus.