What is the limit as x approaches 0+of 2/(sin(x)) ?

The limit as x approaches 0+of 2/(sin(x)) is infinity

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limit as x approaches 0+of 2/(sin(x))

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

\infty

Solution steps

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

For

x

approaching

0

from the right

, x > 0 \Rightarrow sin (x) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to 0 lim (\frac{- sin ( x )}{x})

x \to 0 lim (\frac{b ^{x} - a ^{x}}{x})

x \to \frac{5}{2} lim (\frac{4 x ^{2} - 25}{2 x - 5})

x \to - \infty lim (x^{2} + x)

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

What is the limit as x approaches 0+of 2/(sin(x)) ?
The limit as x approaches 0+of 2/(sin(x)) is infinity