Calculus Examples

$lim_{n \to 8} \cos (n π)$

Step 1

Evaluate the limit.

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Step 1.1

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

$\cos (lim_{n \to 8} n π)$

Step 1.2

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

$\cos (π lim_{n \to 8} n)$

Step 2

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

$\cos (π \cdot 8)$

Step 3

Simplify the answer.

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Step 3.1

Move $8$ to the left of $π$ .

$\cos (8 \cdot π)$

Step 3.2

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\cos (0)$

Step 3.3

The exact value of $\cos (0)$ is $1$ .

$1$