Chapter 1.6, Problem 34E

(a)

To determine

To estimate: The values of $\underset{x\to \infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}$ and $\underset{x\to -\infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}$ by using graph; find the number of horizontal and vertical asymptotes from the graph.

(b)

To determine

To calculate: The numerical estimates of the limits $\underset{x\to \infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}$ and $\underset{x\to -\infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}$ in part(a).

(c)

To determine

To calculate:

The exact value of the limits $\underset{x\to \infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}$ and $\underset{x\to -\infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}$.