Calculus Examples

$lim_{x \to 8} 2 - 5 e^{- x}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $8$ .

$lim_{x \to 8} 2 - lim_{x \to 8} 5 e^{- x}$

Step 2

Evaluate the limit of $2$ which is constant as $x$ approaches $8$ .

$2 - lim_{x \to 8} 5 e^{- x}$

Step 3

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$2 - 5 lim_{x \to 8} e^{- x}$

Step 4

Move the limit into the exponent.

$2 - 5 e^{lim_{x \to 8} - x}$

Step 5

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

$2 - 5 e^{- lim_{x \to 8} x}$

Step 6

Simplify terms.

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Step 6.1

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

$2 - 5 e^{- 8}$

Step 6.2

Simplify each term.

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Step 6.2.1

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

$2 - 5 \frac{1}{e^{8}}$

Step 6.2.2

Combine $- 5$ and $\frac{1}{e^{8}}$ .

$2 + \frac{- 5}{e^{8}}$

Step 6.2.3

Move the negative in front of the fraction.

$2 - \frac{5}{e^{8}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2 - \frac{5}{e^{8}}$

Decimal Form:

$1.99832268 \dots$