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 ) = 270 + 20 t 3 ; t = 1
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 ) = 270 + 20 t 3 ; t = 1
Solution Summary: The author calculates the average rate of change for the function R(t)=270+20t
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.]
4. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.024.
Find the approximations Tη, Mn, and S, to the integral
computer algebra system.)
ASK YOUR TEACHER
PRACTICE ANOTHER
4 39
√
dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a
n
Tn
Mn
Sp
6
12
n
ET
EM
Es
6
12
What observations can you make? In particular, what happens to the errors when n is doubled?
As n is doubled, ET and EM are decreased by a factor of about
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and Es is decreased by a factor of about
6. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.001.
ASK YOUR TEACHER
PRACTICE ANOTHER
Let I =
4
f(x) dx, where f is the function whose graph is shown.
= √ ² F(x
12
4
y
f
1
2
(a) Use the graph to find L2, R2 and M2.
42 =
R₂ =
M₂ =
1
x
3
4
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