Calculus Examples

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

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

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

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

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

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

$lim_{x \to 8} x \cdot \tan (8 lim_{x \to 8} \frac{1}{x})$

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

$lim_{x \to 8} x \cdot \tan (8 \frac{lim_{x \to 8} 1}{lim_{x \to 8} x})$

Evaluate the limit of $1$ which is constant as $x$ approaches $8$ .

$lim_{x \to 8} x \cdot \tan (8 \frac{1}{lim_{x \to 8} x})$

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

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

$8 \cdot \tan (8 \frac{1}{lim_{x \to 8} x})$

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

$8 \cdot \tan (8 (\frac{1}{8}))$

Simplify the answer.

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Cancel the common factor of $8$ .

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Cancel the common factor.

$8 \cdot \tan (8 (\frac{1}{8}))$

Rewrite the expression.

$8 \cdot \tan (1)$

Evaluate $\tan (1)$ .

$8 \cdot 0.01745506$

Multiply $8$ by $0.01745506$ .

$0.13964051$