Chapter 1.1, Problem 14E

Explain the key points and reasons for the establishment of 12.2.5 and 12.2.6

8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.

PLEASE SHOW ME THE RIGHT ANSWER/SOLUTION SHOW ME ALL THE NEDDED STEP   13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.

DO NOT GIVE THE WRONG ANSWER  SHOW ME ALL THE NEEDED STEPS    11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?

please answer by showing all the dfalowing necessary step  DO NOT GIVE ME THE WRONG ANSWER  The sides of a cube of ice are melting at a rate of 1 inch per hour. When its volume is 64 cubic inches, at what rate is its volume changing?

Sox & Sin (px) dx 0

8 L 8 e ipx dx

Find the Taylor polynomial T³(×) for the function f centered at the number a. f(x) = xe-2x a = 0 T3(x) =

For each graph in Figure 16, determine whether f (1) is larger or smaller than the slope of the secant line between x = 1 and x = 1 + h for h > 0. Explain your reasoning