Calculus Examples

e^{- x^{2}}

$e^{- x^{2}}$

Step 1

Find where the expression

e^{- x^{2}}

$e^{- x^{2}}$ 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

- x^{2}

$- x^{2}$ approaches

- \infty

$- \infty$ , the quantity

e^{- x^{2}}

$e^{- x^{2}}$ approaches

0

$0$ .

0

$0$

Step 4

List the horizontal asymptotes:

y = 0

$y = 0$

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

$y = 0$

No Oblique Asymptotes

Step 7