Find the area between the graph of f(t) = -2t for 0 ≤ t ≤ 4 and the t-axis using areas of triangles. Compare your answer with what you get using the Fundamental Theorem of Calculus. (a) Area =

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A: We have given a function that models the height in feet above the surface of the water, h(t)=-16…

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A: Cartesian coordinate (1,-2)

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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: Let,C=

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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 =…

A: Let To calculate the following: (c) If  is an odd  function, then to find .Note:  Since, the student…

Q: At what value(s) of x on the curve y=-7+90x^3-3x^5 does the tangent line have the largest slope?

A: y=-7+90x3

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A: Given:

Q: Question 12 Determine the value of x(t) at t = 0 given its Laplace transform. Choose your answers…

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Q: Evaluate the expression without using a calculator. log 8√√512

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A: Given: To Find: (c) To find the critical points if any of g(x).(d) To find the interval(s) on which…

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A: The given function is

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Q: x+6 (x + 2)2 dx

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A: Since you have asked multiple questions in a single request so we will be answering only first…

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

A: Consider the figure

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A: Given that the amount A of 159 grams of a certain radioactive material remaining after t years is

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Q: 5. The compound amount, 4, accrued with quarterly compounding ^=P(1+4)". where P is the principal, r…

A: To find the time it takes for the money to double with quarterly compounding, you can use the…

Q: 2. f(x) = = 1 1+72) [0,4], n = 4 , 1+x²¹

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A: The initial value problem is given as,solve the problem.

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A: The velocity of a car is  for all .The aim is to find the position of the car.

Q: Use the Comparison Test to determine the convergence of the following series. n=1 n sin² n n³ + 1

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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: The given function is

Q: The equation of a hyperbola is (y + 3)2 - 16(x-3)² = 16. a) Find the center, vertices, transverse…

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Q: (i) Find the derivative of the function. esin x COS X In(1+2v) dv.

A: To find the derivative of the following function.

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Q: Find the integral. Use C for the constant of integration. J cos(9t) sin(9t) dt

A: To find the following integral.

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A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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A: Let, .We know that,

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: antiderivative. Use C for the constant of integration. 1 3 cos² (4x) F(x) = (In(|sec (4x) +…

A: Given The aim is to find the antiderivative of .