Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of R ( t ) over the time intervals [ t , t + h ] , where t is as indicated and h = 0 , 0.1 , and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] R ( t ) = 60 t − 2 t 2 ; t = 3
Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of R ( t ) over the time intervals [ t , t + h ] , where t is as indicated and h = 0 , 0.1 , and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] R ( t ) = 60 t − 2 t 2 ; t = 3
Solution Summary: The author calculates the average rate of change for the function R(t)=60t-2t
Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of
R
(
t
)
over the time intervals
[
t
,
t
+
h
]
, where t is as indicated and
h
=
0
,
0.1
,
and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [HINT: See Example 1.]
Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001.
f(x) = 13x2; a = 0
h = 1
h = 0.1
h = 0.01
h = 0.001
h = 0.0001
Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001.
f(x) = 38x2; a = 0
h=1
h=0.1
h=0.01
In a certain state, the sales tax T on the amount of taxable goods is 5% of the value of the goods purchased (x), where both T and x are measured in dollars. (a) Express T as a function of x.
Chapter 10 Solutions
Finite Mathematics and Applied Calculus (MindTap Course List)
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