Calculus Examples

$lim_{x \to 8} 3 x e^{x}$

Step 1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 8} x e^{x}$

Step 2

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

$3 lim_{x \to 8} x \cdot lim_{x \to 8} e^{x}$

Step 3

Move the limit into the exponent.

$3 lim_{x \to 8} x \cdot e^{lim_{x \to 8} x}$

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 $x$ .

$3 \cdot 8 \cdot e^{lim_{x \to 8} x}$

Step 4.2

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

$3 \cdot 8 \cdot e^{8}$

Step 5

Multiply $3$ by $8$ .

$24 e^{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$24 e^{8}$

Decimal Form:

$71542.99168900 \dots$