(a) Find the approximations
T_(10)
and
M_(10)
for
\int_1^2 31e^((1)/(x))dx
. (Round your answers to six decimal places.)
T_(10)=
M_(10)=
q,
◻
(b) Estimate the errors in the approximations of part (a) using the smallest possible value for
K
according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.)
|E_(T)|<=
|E_(M)|<=
q,
◻
(c) Using the values of
K
from part (b), how large do we have to choose
n
so that the approximations
T_(n)
and
M_(n)
to the integral in part (a) are accurate to within 0.0001 ? For
T_(n^(')),n=
x
. For
M_(n^('))n=
x
. Do the following with the given information.
\int_0^1 27cos(x^(2))dx
(a) Find the approximations
T_(8)
and
M_(8)
for the given integral. (Round your answer to six decimal places.)
T_(8)=,✓ Great work.
M_(8)=,✓ Great jobt
(b) Estimate the errors in the approximations
T_(8)
and
M_(8)
in part (a). (Use the fact that the range of the sine and cosine functions is bounded by
!=1
to estimate the maximum error. Round your answer to seven decimal places.)
|E_(T)|<=
|E_(M)|<=
q,
q,
(c) How large do we have to choose
n
so that the approximations
T_(n)
and
M_(n)
to the integral are accurate to within 0.0001 ? (Use the fact that the range of the sine and cosine functions is bounded by
-1
to estimate the maximum error.)
n>=
q,
\times
for
T_(n)
n>=
◻
\times
for
M_(n)