Calculus Examples

$\frac{lim_{x \to 8} 12 e^{x}}{2 x^{2}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$\frac{12 lim_{x \to 8} e^{x}}{2 x^{2}}$

Step 1.2

Move the limit into the exponent.

$\frac{12 e^{lim_{x \to 8} x}}{2 x^{2}}$

Step 2

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

$\frac{12 e^{8}}{2 x^{2}}$

Step 3

Cancel the common factor of $12$ and $2$ .

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Step 3.1

Factor $2$ out of $12 e^{8}$ .

$\frac{2 (6 e^{8})}{2 x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (6 e^{8})}{2 (x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (6 e^{8})}{2 x^{2}}$

Step 3.2.3

Rewrite the expression.

$\frac{6 e^{8}}{x^{2}}$