Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Multiply $π - x$ by $1$ .

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

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $π$ .

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

Step 1.3

Evaluate the limit of $π$ which is constant as $x$ approaches $π$ .

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

Step 2

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

$\frac{π - π}{\sin (x)}$

Step 3

Simplify the answer.

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Step 3.1

Subtract $π$ from $π$ .

$\frac{0}{\sin (x)}$

Step 3.2

Separate fractions.

$\frac{0}{1} \cdot \frac{1}{\sin (x)}$

Step 3.3

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

$\frac{0}{1} \csc (x)$

Step 3.4

Divide $0$ by $1$ .

$0 \csc (x)$

Step 3.5

Multiply $0$ by $\csc (x)$ .

$0$