Calculus Examples

$\frac{lim_{x \to 0} \ln (\cos (x))}{x^{2}}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the limit inside the logarithm.

$\frac{\ln (lim_{x \to 0} \cos (x))}{x^{2}}$

Step 1.2

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

$\frac{\ln (\cos (lim_{x \to 0} x))}{x^{2}}$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{\ln (\cos (0))}{x^{2}}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

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

$\frac{\ln (1)}{x^{2}}$

Step 3.1.2

The natural logarithm of $1$ is $0$ .

$\frac{0}{x^{2}}$

Step 3.2

Divide $0$ by $x^{2}$ .

$0$