What is the limit as x approaches 0+of 1/(sin(2x)) ?

The limit as x approaches 0+of 1/(sin(2x)) is infinity

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limit as x approaches 0+of 1/(sin(2x))

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

\infty

Solution steps

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

For

x

approaching

0

from the right

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

The denominator is a positive quantity approaching 0 from the right

= \infty

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

x \to 3 lim (\frac{3 + x}{2 x - 6})

x \to 0 lim ((1 + ∣ x ∣)^{\frac{1}{x}})

x \to 1 lim (3 x + 4)

x \to 0 lim ((sin (x)) ln (x))

What is the limit as x approaches 0+of 1/(sin(2x)) ?
The limit as x approaches 0+of 1/(sin(2x)) is infinity