Chapter 5.6, Problem 62E

(a)

To determine

To calculate: The type of the indeterminate form of the function $\underset{x\to \infty }{\lim }\left(x-\sqrt{x^2+1}\right)$ by direct substitution.

(b)

To determine

To calculate: The limit $\underset{x\to \infty }{\lim }\left(x-\sqrt{x^2+1}\right)$, using L’ Hospital’s Rule if necessary.

(c)

To determine

To graph: The graph of the provided function $\underset{x\to \infty }{\lim }\left(x-\sqrt{x^2+1}\right)$, using graphing utility and verify the result in part (b).