Calculus Examples

$\frac{lim_{x \to 8} e^{2 x}}{4 x^{3} + 2 x - 5}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$\frac{e^{lim_{x \to 8} 2 x}}{4 x^{3} + 2 x - 5}$

Step 1.2

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\frac{e^{2 lim_{x \to 8} x}}{4 x^{3} + 2 x - 5}$

Step 2

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

$\frac{e^{2 \cdot 8}}{4 x^{3} + 2 x - 5}$

Step 3

Multiply $2$ by $8$ .

$\frac{e^{16}}{4 x^{3} + 2 x - 5}$