Calculus Examples

$f (x) = e^{- \frac{x^{2}}{2}}$

Step 1

Find where the expression $e^{- \frac{x^{2}}{2}}$ is undefined.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

Since the exponent $- \frac{x^{2}}{2}$ approaches $- \infty$ , the quantity $e^{- \frac{x^{2}}{2}}$ approaches $0$ .

$0$

Step 4

List the horizontal asymptotes:

$y = 0$

Step 5

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

Step 6

This is the set of all asymptotes.

No Vertical Asymptotes

Horizontal Asymptotes: $y = 0$

No Oblique Asymptotes

Step 7