X = = 3 sin(t), y = 4 cos(t), 0 < t < 2π (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. (c) Find an equation of the tangent to the curve at t = 0.

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A: The objective of this question is to find the critical numbers of the function f(x) = -3x^2 + 36x…

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Q: Find y'' if y=-8 cos x. OA. y'=8 sin x OB. y'= -8 cos x OC. y'= 8 cos x OD. y'= -8 sin x

A: Explaination of answer is as follows

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A:

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A: The graph of the function g'(x) is shown as,

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A: Limit does not exist when the left hand limit and right hand limit is not same.

Q: 2 2 Find the area of the region between the curves y = 4x² - 4 and y=-3x +3 from x= -1 to x= 1.

A: The required area is the shaded region in the graph

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A: ...(1)

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Q: What is the second derivative x³ - 5x² + x = 0? A. 3x² - 5x B. 10x-5 C. 3x + 10 D. 6x-10

A: The given equation is Let

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Q: 6. Let So f(x) dx = 12, 5 Calculate the following integrals. (a) [°*3f(x)dx = (b) *2f(x) – g(x)dx =…

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Q: 2. For f(x)=√14-2x (a). find the domain. Write your answer in interval notation. (b). Graph…

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Q: Consider the following. f(x) = 48x − 4x2 Find  f '(x). f '(x) =        Find the critical…

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A: The problem is given as,such that

Q: Question Find the average rate of change of the function in the graph shown below between x = -1 and…

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Q: 2 x(x²-1) dx x²+1

A: To evaluate the following integral.

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. S² dt

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Q: Find y'' if y=-6 cos x. OA. y' = 6 sin x OB. y' = 6 cos x OC. y'= -6 cos x OD. y'= -6 sin x

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Q: hich of the following integration formula is incorrect? O I sin x + I see 2 x² +1 sec² x cot x csc x…

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Q: Evaluate the following indefinite integral. S dt 16-48

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Q: Find the value of (fog)' at the given value of x. Assume that f'(3)=8, g'(4) = -6, g(4)=3, and y =…

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Q: Refer to the graph shown below and evaluate Ĵ 1941 CH - 4 f(t)dt.

A: Consider the figure

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Q: 256x The volume of a sphere is increasing at a rate of 3 cm³/sec. Find the rate of change of its…

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Q: Find the arc length of the graph of (y − 1)3 = x2 on the interval [0, 8]

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Q: Considering the definition of f(x) below, find lim f(x). x-*6 Select the correct answer below: O -56…

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Q: Given 6xy= 2 + y³ ,  a) Find the coordinates of a point on the curve at which the line tangent to…

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Q: Time (secs) 0 30 60 90 120 150 180 Speed (mi/secs) 0.00 0.03 0.08 0.16 0.27 0.42 0.65 9. The table…

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