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

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

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

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

\infty

Solution steps

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

Express with sin, cos

= x \to 0 + lim (\frac{1}{x sin ( 2 x )})

For

x

approaching

0

from the right

, x > 0 \Rightarrow x sin (2 x) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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