Calculus Examples

\frac{e^{x} + x^{3} ln (x)}{e^{x} - ln (x)}

$\frac{e^{x} + x^{3} \ln (x)}{e^{x} - \ln (x)}$

Step 1

Find where the expression

\frac{e^{x} + x^{3} ln (x)}{e^{x} - ln (x)}

$\frac{e^{x} + x^{3} \ln (x)}{e^{x} - \ln (x)}$ is undefined.

x \leq 0

$x \leq 0$

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

Since the limit does not exist, there are no horizontal asymptotes.

No Horizontal Asymptotes

Step 4

No oblique asymptotes are present for logarithmic and trigonometric functions.

No Oblique Asymptotes

Step 5

This is the set of all asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

Step 6