Calculus Examples

$\frac{lim_{x \to 1} \ln (x)}{\sin (π x)}$

Step 1

Move the limit inside the logarithm.

$\frac{\ln (lim_{x \to 1} x)}{\sin (π x)}$

Step 2

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

$\frac{\ln (1)}{\sin (π x)}$

Step 3

Simplify the answer.

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Step 3.1

Separate fractions.

$\frac{\ln (1)}{1} \cdot \frac{1}{\sin (π x)}$

Step 3.2

Convert from $\frac{1}{\sin (π x)}$ to $\csc (π x)$ .

$\frac{\ln (1)}{1} \csc (π x)$

Step 3.3

Divide $\ln (1)$ by $1$ .

$\ln (1) \csc (π x)$

Step 3.4

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

$0 \csc (π x)$

Step 3.5

Multiply $0$ by $\csc (π x)$ .

$0$