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

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

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

x \to 0 lim (\frac{tan ( π x )}{x})

π

Decimal

3.14159 \dots

Solution steps

x \to 0 lim (\frac{tan ( π x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( π x ) π}{1})

= x \to 0 lim (\frac{sec ^{2} ( π x ) π}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( π 0 ) π}{1}

Simplify

\frac{sec ^{2} ( π 0 ) π}{1} : π

= π

\frac{d}{d x} (e^{y z (x)})

x \to 2 lim ([4 f (- 8) + g (2)])

n = 1 \sum \infty \frac{- 2 + 3 ^{n}}{2 ^{2 n}}

n = 1 \sum \infty n 19

\frac{d}{d θ} (\frac{2}{6 cos ( θ ) + 7 sin ( θ )})

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