Calculus Examples

$lim_{x \to \frac{3 π}{4}} 2 \cos (x)$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to \frac{3 π}{4}} \cos (x)$

Step 1.2

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

$2 \cos (lim_{x \to \frac{3 π}{4}} x)$

Step 2

Evaluate the limit of $x$ by plugging in $\frac{3 π}{4}$ for $x$ .

$2 \cos (\frac{3 π}{4})$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

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.

$2 (- \cos (\frac{π}{4}))$

Step 3.2

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$2 (- \frac{\sqrt{2}}{2})$

Step 3.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.1

Move the leading negative in $- \frac{\sqrt{2}}{2}$ into the numerator.

$2 \frac{- \sqrt{2}}{2}$

Step 3.3.2

Cancel the common factor.

$2 \frac{- \sqrt{2}}{2}$

Step 3.3.3

Rewrite the expression.

$- \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{2}$

Decimal Form:

$- 1.41421356 \dots$