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

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

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

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

1

Solution steps

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

x \to 0 lim (1) = 1

x \to 0 lim (x csc (x)) = 1

= \frac{1}{1}

Simplify

= 1

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