(Solved): (a) Find the approximations T_(10) and M_(10) for \int_1^2 31e^((1)/(x))dx. (Round your answers to s ...

(a) Find the approximations

and

for

. (Round your answers to six decimal places.)

(b) Estimate the errors in the approximations of part (a) using the smallest possible value for

according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.)

(c) Using the values of

from part (b), how large do we have to choose

so that the approximations

and

to the integral in part (a) are accurate to within 0.0001 ? For

. For

. Do the following with the given information.

(a) Find the approximations

and

for the given integral. (Round your answer to six decimal places.)

(b) Estimate the errors in the approximations

and

in part (a). (Use the fact that the range of the sine and cosine functions is bounded by

to estimate the maximum error. Round your answer to seven decimal places.)

(c) How large do we have to choose

so that the approximations

and

to the integral are accurate to within 0.0001 ? (Use the fact that the range of the sine and cosine functions is bounded by

to estimate the maximum error.)

for

for