Calculus Examples

$lim_{x \to 8} x^{17} e^{- x}$

Step 1

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

$lim_{x \to 8} x^{17} \cdot lim_{x \to 8} e^{- x}$

Step 2

Move the exponent $17$ from $x^{17}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 8} x)}^{17} \cdot lim_{x \to 8} e^{- x}$

Step 3

Move the limit into the exponent.

${(lim_{x \to 8} x)}^{17} \cdot e^{lim_{x \to 8} - x}$

Step 4

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

${(lim_{x \to 8} x)}^{17} \cdot e^{- lim_{x \to 8} x}$

Step 5

Evaluate the limits by plugging in $8$ for all occurrences of $x$ .

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Step 5.1

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

$8^{17} \cdot e^{- lim_{x \to 8} x}$

Step 5.2

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

$8^{17} \cdot e^{- 8}$

Step 6

Simplify the answer.

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Step 6.1

Raise $8$ to the power of $17$ .

$2251799813685250 \cdot e^{- 8}$

Step 6.2

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

$2251799813685250 \cdot \frac{1}{e^{8}}$

Step 6.3

Combine $2251799813685250$ and $\frac{1}{e^{8}}$ .

$\frac{2251799813685250}{e^{8}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2251799813685250}{e^{8}}$

Decimal Form:

$755394683009.241$