Calculus Examples

$lim_{x \to 8} \frac{\tan (x)}{e^{x}}$

Step 1

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

$\frac{lim_{x \to 8} \tan (x)}{lim_{x \to 8} e^{x}}$

Step 2

Move the limit inside the trig function because tangent is continuous.

$\frac{\tan (lim_{x \to 8} x)}{lim_{x \to 8} e^{x}}$

Step 3

Move the limit into the exponent.

$\frac{\tan (lim_{x \to 8} x)}{e^{lim_{x \to 8} x}}$

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 $x$ .

$\frac{\tan (8)}{e^{lim_{x \to 8} x}}$

Step 4.2

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

$\frac{\tan (8)}{e^{8}}$

Step 5

Simplify the answer.

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Step 5.1

Evaluate $\tan (8)$ .

$\frac{0.14054083}{e^{8}}$

Step 5.2

Replace $e$ with an approximation.

$\frac{0.14054083}{{2.71828182}^{8}}$

Step 5.3

Raise $2.71828182$ to the power of $8$ .

$\frac{0.14054083}{2980.95798704}$

Step 5.4

Divide $0.14054083$ by $2980.95798704$ .

$0.00004714$