What is the limit as x approaches 0 of (sin(pix))/x ?

The limit as x approaches 0 of (sin(pix))/x is pi

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limit as x approaches 0 of (sin(pix))/x

x \to 0 lim (\frac{sin ( π x )}{x})

π

Decimal

3.14159 \dots

Solution steps

x \to 0 lim (\frac{sin ( π x )}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( π x ) π}{1})

Plug in the value

x = 0

= \frac{cos ( π 0 ) π}{1}

Simplify

\frac{cos ( π 0 ) π}{1} : π

= π

What is the limit as x approaches 0 of (sin(pix))/x ?
The limit as x approaches 0 of (sin(pix))/x is pi