What is the limit as x approaches pi/2 of x/(sin(x)) ?

The limit as x approaches pi/2 of x/(sin(x)) is pi/2

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limit as x approaches pi/2 of x/(sin(x))

x \to \frac{π}{2} lim (\frac{x}{sin ( x )})

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

x \to \frac{π}{2} lim (\frac{x}{sin ( x )})

Plug in the value

x = \frac{π}{2}

= \frac{\frac{π}{2}}{sin ( \frac{π}{2} )}

Simplify

\frac{\frac{π}{2}}{sin ( \frac{π}{2} )} : \frac{π}{2}

= \frac{π}{2}

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

x \to 2 lim ((3 x^{2} - 5 x - 5)^{2})

x \to 0 lim (x^{3} - x)

x \to 0 lim (\frac{x + 2 sin ( x )}{x})

What is the limit as x approaches pi/2 of x/(sin(x)) ?
The limit as x approaches pi/2 of x/(sin(x)) is pi/2