Calculus Examples

$lim_{x \to 1} \frac{\ln (x)}{\sin (6 π)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\frac{1}{\sin (6 π)}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{\sin (6 π)} lim_{x \to 1} \ln (x)$

Step 1.2

Move the limit inside the logarithm.

$\frac{1}{\sin (6 π)} \ln (lim_{x \to 1} x)$

Step 2

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

$\frac{1}{\sin (6 π)} \ln (1)$

Step 3

Simplify the answer.

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Step 3.1

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

$\frac{1}{\sin (0)} \ln (1)$

Step 3.2

The exact value of $\sin (0)$ is $0$ .

$\frac{1}{0} \ln (1)$

Step 3.3

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{1}{0} \ln (1)$

Step 4

The expression contains a division by $0$ . The expression is undefined.

Undefined