Chapter 2.6, Problem 54E

(a) Graph the function

$f(x)=\frac{\sqrt{2x^2+1}}{3x-5}$

How many horizontal and vertical asymptotes do you observe? Use the graph to estimate the values of the limits

$\underset{x\to \infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}\text{and}\underset{x\to -\infty }{\lim }\frac{\sqrt{2x^2+1}}{3x-5}$

(b) By calculating values of f(x), give numerical estimates of the limits in part (a).

(c) Calculate the exact values of the limits in part (a). Did you get the same value or different values for these two limits? [In view of your answer to part (a), you might have to check your calculation for the second limit.]