Calculus Examples

$lim_{x \to 8} e^{- x}$

Step 1

Move the limit into the exponent.

$e^{lim_{x \to 8} - x}$

Step 2

Move the term $- 1$ outside of the limit because it is constant with respect to $x$ .

$e^{- lim_{x \to 8} x}$

Step 3

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$e^{- 8}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{e^{8}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{e^{8}}$

Decimal Form:

$0.00033546 \dots$