Chapter 4.5, Problem 66E

Using the Definition of Limits at Infinity The graph of $f(x)=\frac{6x}{\sqrt{x^2+2}}$ is shown (see figure).

(a) Find $L=\underset{x\to \infty }{\lim }f(x)$ and $K=\underset{x\to -\infty }{\lim }f(x)$.

(b) Determine $x_1$ and $x_2$ in terms of $\epsilon$.

(c) Determine M, where $M>0$, such that $\left|f(x)-L\right|<\epsilon$ for $x>M$.

(d) Determine N, where $N>0$, such that $\left|f(x)-K\right|<\epsilon$ for

$x>N$.