20. Let f(t) 1/t for t = 0. a. Find the average rate of change of f with respect to t over the intervals (i) from t = 2 to t = 3, and (ii) from t = 2 to t = T. b. Make a table of values of the average rate of change of f with respect to t over the interval [2, T], for some values of T ap- proaching 2, say T = 2.1, 2.01, 2.001, 2.0001, 2.00001, and 2.000001. = c. What does your table indicate is the rate of change of f with respect to t at t = 2?
20. Let f(t) 1/t for t = 0. a. Find the average rate of change of f with respect to t over the intervals (i) from t = 2 to t = 3, and (ii) from t = 2 to t = T. b. Make a table of values of the average rate of change of f with respect to t over the interval [2, T], for some values of T ap- proaching 2, say T = 2.1, 2.01, 2.001, 2.0001, 2.00001, and 2.000001. = c. What does your table indicate is the rate of change of f with respect to t at t = 2?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![20. Let f(t) = 1/t for t + 0.
a. Find the average rate of change of f with respect to t over the
intervals (i) from t = 2 to t = 3, and (ii) from t = 2 to t = T.
b. Make a table of values of the average rate of change of f with
respect to t over the interval [2, T], for some values of T ap-
proaching 2, say T = 2.1, 2.01, 2.001, 2.0001, 2.00001, and
2.000001.
c. What does your table indicate is the rate of change of f with
respect to t at t = 2?
d. Calculate the limit as T approaches 2 of the average rate of
change of f with respect to t over the interval from 2 to T. You
will have to do some algebra before you can substitute T = 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1477405-e117-417e-a6fe-7ae78ca4f539%2F2a75a98e-c497-4aec-b4bb-9551ff5da6cf%2F2d653wt_processed.png&w=3840&q=75)
Transcribed Image Text:20. Let f(t) = 1/t for t + 0.
a. Find the average rate of change of f with respect to t over the
intervals (i) from t = 2 to t = 3, and (ii) from t = 2 to t = T.
b. Make a table of values of the average rate of change of f with
respect to t over the interval [2, T], for some values of T ap-
proaching 2, say T = 2.1, 2.01, 2.001, 2.0001, 2.00001, and
2.000001.
c. What does your table indicate is the rate of change of f with
respect to t at t = 2?
d. Calculate the limit as T approaches 2 of the average rate of
change of f with respect to t over the interval from 2 to T. You
will have to do some algebra before you can substitute T = 2.
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