Calculus Examples

$lim_{x \to 8} x^{4} e^{x}$

Step 1

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

$lim_{x \to 8} x^{4} \cdot lim_{x \to 8} e^{x}$

Step 2

Move the exponent $4$ from $x^{4}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 8} x)}^{4} \cdot lim_{x \to 8} e^{x}$

Step 3

Move the limit into the exponent.

${(lim_{x \to 8} x)}^{4} \cdot e^{lim_{x \to 8} x}$

Step 4

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

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Step 4.1

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

$8^{4} \cdot e^{lim_{x \to 8} x}$

Step 4.2

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

$8^{4} \cdot e^{8}$

Step 5

Raise $8$ to the power of $4$ .

$4096 e^{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4096 e^{8}$

Decimal Form:

$12210003.9149229$