24. Let f(t) = 1/t for t + 0. a. Find the average rate of change of f with respect to 1 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.
24. Let f(t) = 1/t for t + 0. a. Find the average rate of change of f with respect to 1 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.
Chapter2: Functions And Their Graphs
Section2.3: Analyzing Graphs Of Functions
Problem 6ECP
Related questions
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![24. Let f(t) = 1/t for t + 0.
a. Find the average rate of change of f with respect to 1 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%2Fdea578aa-a135-4a56-982a-883ce090d506%2F5d674d21-725b-4435-88c8-7dfdf7e96329%2F8t43lw_processed.png&w=3840&q=75)
Transcribed Image Text:24. Let f(t) = 1/t for t + 0.
a. Find the average rate of change of f with respect to 1 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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