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

The limit as x approaches 0 of x/(sin(pix)) is 1/pi

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

x \to 0 lim (\frac{x}{sin ( π x )})

\frac{1}{π}

Decimal Notation

0.31830 \dots

Solution steps

x \to 0 lim (\frac{x}{sin ( π x )})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{1}{cos ( π 0 ) π}

cos (π 0) π = π

= \frac{1}{π}

x \to - \infty lim (x^{5})

x \to 1 lim (3 x^{2} + 2 x + 1)

\frac{d}{d x} (x cos (\frac{1}{x}))

\int \frac{2 x + 21}{2 x ^{2} + 9 x - 5} d x

x \to - 1 lim ((x + 2 x^{3})^{4})

What is the limit as x approaches 0 of x/(sin(pix)) ?
The limit as x approaches 0 of x/(sin(pix)) is 1/pi