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 Notation

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})

= 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

\int \frac{1}{x ( ln ( x ) ) ^{5}} d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 3 x^{3}))

\int \frac{1}{( x + 3 ) ln ( x + 3 )} d x

e^{a x}

\frac{d}{d x} (\frac{1}{3 - x})

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