Please show Work. Written, Explain, No Shortcuts The average value of f(x) = 3x2

Question

Please show Work. Written, Explain, No Shortcuts

The average value of f(x) = 3x2 + 1 on the interval [2,4] is: 29 66 58 36 Which point x1,x2,x3, or x4, on the graph is the best choice to serve as the point guaranteed br the Mean Value Theorem for Integrals? X1 x2 x3 x4 Find a point c for the Mean Value Theorem for integrals for f(x) = x2 - 2x on [2,5]. 18 6 no such c exists The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. x2 + (y - 1)2 = 1; about the y axis Select the correct answer. V = 5/3 pi V = 2/3 pi V = 1/3 pi V = 4/3 pi V = 7/3 pi If 132 J of work are needed to stretch a string from 9 cm to 12 cm and another 588 J are needed to stretch it from 12 cm to 19 cm. What is the natural length of the spring? Select the correct answer. 6 cm 5 cm 3 cm 4 cm 1 cm Evaluate to the the area from 1 to 5 under the graph of f(x) = 4/x using four approximating rectangles and right endpoints. Select correct answer. 5.13 6.65 5.83 3.65 4.23 Evaluate the Riemann sum for f(r) 2 - r2 , 0 le r le 2, with four subintervals, taking the sample points to be right endpoints. Select the correct answer. 0.25 1.5 2.5 0.36 0.2 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function Select the correct answer. dg(x)/dx = -8 tan x dg(x)/dx = 8 tan 7 dg(x)/dx = 8 tan x dg(x)/dx = -8x tan 8x dg(x)/dx = -7 tan 7x

Explanation / Answer

37d

38b

39a

40b

41a

42d

43b

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