Chapter 2.6, Problem 88E

Asymptotes of a function containing exponentials Let $f(x)=\frac{2e^x+5e^{3x}}{e^{2x}-e^{3x}}$. Analyze $\underset{x\to 0^{-}}{\lim }f(x),\underset{x\to 0^{+}}{\lim }f(x),\underset{x\to -\infty }{\lim }f(x)$, and $\underset{x\to \infty }{\lim }f(x)$. Then give the horizontal and vertical asymptotes of f. Plot f to verify your results.