Chapter 8.7, Problem 83E

(a)

To determine

Why L’HospitaL’s rule can’t be used to determine the limit $\underset{x\to \infty }{\lim }\frac{x}{\sqrt{x^2+1}}$.

(b)

To determine

To calculate: The limit $\underset{x\to \infty }{\lim }\frac{x}{\sqrt{x^2+1}}$ analytically.

(c)

To determine

To graph: The function $\frac{x}{\sqrt{x^2+1}}$ and verify $\underset{x\to \infty }{\lim }\frac{x}{\sqrt{x^2+1}}=1$ using a graphing utility.