What is the limit as x approaches 0 of 1/(csc(x)) ?

The limit as x approaches 0 of 1/(csc(x)) is 0

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limit as x approaches 0 of 1/(csc(x))

x \to 0 lim (\frac{1}{csc ( x )})

0

Solution steps

x \to 0 lim (\frac{1}{csc ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to 0} ( 1 )}{lim _{x \to 0} ( csc ( x ) )}

x \to 0 lim (1) = 1

x \to 0 lim (csc (x)) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

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\frac{\partial}{\partial y} (\frac{x ^{2}}{y})

\int sin (x) + cos (x) d x

y = 2 x - \frac{2}{x}

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What is the limit as x approaches 0 of 1/(csc(x)) ?
The limit as x approaches 0 of 1/(csc(x)) is 0