Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

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

$\cos (\frac{1}{8})$

Step 3

Evaluate $\cos (\frac{1}{8})$ .

$0.99219766$