What is the limit as x approaches 0+of (csc(4x))/x ?

The limit as x approaches 0+of (csc(4x))/x is infinity

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limit as x approaches 0+of (csc(4x))/x

x \to 0 + lim (\frac{csc ( 4 x )}{x})

\infty

Solution steps

x \to 0 + lim (\frac{csc ( 4 x )}{x})

Express with sin, cos

= x \to 0 + lim (\frac{1}{x sin ( 4 x )})

For

x

approaching

0

from the right

, x > 0 \Rightarrow x sin (4 x) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to 0 lim (+ (\frac{∣ x ∣}{x}))

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

x \to 1 - lim (\frac{sin ( x )}{x})

x \to 0 lim (\frac{x}{a} \cdot [\frac{b}{x}])

x \to - 1 + lim (\frac{4 - x}{x + 1})

What is the limit as x approaches 0+of (csc(4x))/x ?
The limit as x approaches 0+of (csc(4x))/x is infinity