Chapter 8.4, Problem 41E

(a)

To determine

To approximate: The definite integral ${\displaystyle \underset{0}{\overset{b}{\int }}{e}^{-0.00001x}}dx$ using calculator for $b=10,50,100\text{and }\text{1000}$.

(b)

To determine

Whether the integral ${\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-0.00001x}}dx$ based on part (a) is convergent or divergent.

(c)

To determine

To find: The value for which the integral ${\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-0.00001x}}dx$ is actually convergent.