Calculus Examples

$lim_{x \to π} \cos (7 x)$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$\cos (lim_{x \to π} 7 x)$

Step 1.2

Move the term $7$ outside of the limit because it is constant with respect to $x$ .

$\cos (7 lim_{x \to π} x)$

Step 2

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

$\cos (7 π)$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

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

$\cos (π)$

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 $1$ .

$- 1$