What is the limit as x approaches 0 of 1/(csc^3(x)) ?

The limit as x approaches 0 of 1/(csc^3(x)) is 0

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limit as x approaches 0 of 1/(csc^3(x))

x \to 0 lim (\frac{1}{csc ^{3} ( x )})

0

Solution steps

x \to 0 lim (\frac{1}{csc ^{3} ( 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 ^{3} ( x ) )}

x \to 0 lim (1) = 1

x \to 0 lim (csc^{3} (x)) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to 0 lim (x sec (x))

θ \to \infty lim (cos (θ))

x \to 1 - lim (\frac{x ^{2}}{1 - x ^{2}})

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

x \to 4 lim (\frac{x ^{2}}{21})

What is the limit as x approaches 0 of 1/(csc^3(x)) ?
The limit as x approaches 0 of 1/(csc^3(x)) is 0