Calculus Examples

$lim_{x \to 1} \cos (\frac{π x}{3})$

Step 1

Evaluate the limit.

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Step 1.1

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

$\cos (lim_{x \to 1} \frac{π x}{3})$

Step 1.2

Move the term $\frac{π}{3}$ outside of the limit because it is constant with respect to $x$ .

$\cos (\frac{π}{3} lim_{x \to 1} x)$

Step 2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\cos (\frac{π}{3} \cdot 1)$

Step 3

Simplify the answer.

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Step 3.1

Multiply $\frac{π}{3}$ by $1$ .

$\cos (\frac{π}{3})$

Step 3.2

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$