Calculus Examples

$lim_{x \to 7} \cos (\frac{π x}{3})$

Step 1

Evaluate the limit.

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Step 1.1

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

$\cos (lim_{x \to 7} \frac{π x}{3})$

Step 1.2

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

$\cos (\frac{π}{3} lim_{x \to 7} x)$

Step 2

Evaluate the limit of $x$ by plugging in $7$ for $x$ .

$\cos (\frac{π}{3} \cdot 7)$

Step 3

Simplify the answer.

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Step 3.1

Combine $\frac{π}{3}$ and $7$ .

$\cos (\frac{π \cdot 7}{3})$

Step 3.2

Move $7$ to the left of $π$ .

$\cos (\frac{7 \cdot π}{3})$

Step 3.3

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

$\cos (\frac{π}{3})$

Step 3.4

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:

$0.5$