Calculus Examples

$lim_{x \to 1} \cos (π x)$

Step 1

Evaluate the limit.

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Step 1.1

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

$\cos (lim_{x \to 1} π x)$

Step 1.2

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

$\cos (π lim_{x \to 1} x)$

Step 2

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

$\cos (π \cdot 1)$

Step 3

Simplify the answer.

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Step 3.1

Multiply $π$ by $1$ .

$\cos (π)$

Step 3.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$- \cos (0)$

Step 3.3

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

$- 1 \cdot 1$

Step 3.4

Multiply $- 1$ by $1$ .

$- 1$