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

y^{^{''}} - y = 0, y (0) = 2

x + y = - 3, x + 9 = y^{2}

\frac{d}{d x} (cos (x - \frac{π}{2}))

\frac{e ^{5 x}}{x ^{20}}

y = 3 x^{\frac{1}{2}} + x^{\frac{3}{2}}

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