Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

$\frac{\sin (π \cdot 1)}{x - 1}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $π$ by $1$ .

$\frac{\sin (π)}{x - 1}$

Step 3.1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

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

Step 3.1.3

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

$\frac{0}{x - 1}$

Step 3.2

Divide $0$ by $x - 1$ .

$0$