Calculus Examples

$lim_{n \to 8} \cos (\frac{2}{n})$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$\cos (lim_{n \to 8} \frac{2}{n})$

Step 1.2

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

$\cos (2 lim_{n \to 8} \frac{1}{n})$

Step 1.3

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

$\cos (2 \frac{lim_{n \to 8} 1}{lim_{n \to 8} n})$

Step 1.4

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

$\cos (2 \frac{1}{lim_{n \to 8} n})$

Step 2

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

$\cos (2 (\frac{1}{8}))$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $8$ .

$\cos (2 \frac{1}{2 (4)})$

Step 3.1.2

Cancel the common factor.

$\cos (2 \frac{1}{2 \cdot 4})$

Step 3.1.3

Rewrite the expression.

$\cos (\frac{1}{4})$

Step 3.2

Evaluate $\cos (\frac{1}{4})$ .

$0.96891242$