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# (a) Find the approximations $T_{10}$ and $M_{10}$ for $\displaystyle \int_1^2 e^{\frac{1}{x}}\ dx$.(b) Estimate the errors in the approximations of part (a).(c) 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?

## a. $T_{10}=2.021976$$M_{10}=2.019102b. \left|E_{T}\right| \leq .0068$$\left|E_{M}\right| \leq .0034$ c. Trapezoidal rule: $n=83, \quad$ Midpoint rule: $n=59$

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