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

\int \frac{1}{100 x ^{2} + 1} d x

y^{^{'}} = \frac{y}{x} + \frac{6 x ^{3}}{y} cos (x^{2})

y = 2 x + x^{2}, (- 2, 0)

\int x \cdot x d x

y = (x^{2} - 7 x)^{2}

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