Calculus Examples

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

Step 1

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

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

Step 2

Move the limit into the exponent.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

$8 \cdot e^{8}$

$8 e^{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$8 e^{8}$

Decimal Form:

$23847.663896\overline{3}$