What is the limit as x approaches pi+of (sqrt(x))/(csc(x)) ?

The limit as x approaches pi+of (sqrt(x))/(csc(x)) is 0

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limit as x approaches pi+of (sqrt(x))/(csc(x))

x \to π + lim (\frac{x}{csc ( x )})

0

Solution steps

x \to π + lim (\frac{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 π +} ( x )}{lim _{x \to π +} ( csc ( x ) )}

x \to π + lim (x) = π

x \to π + lim (csc (x)) = - \infty

= \frac{π}{- \infty}

Apply Infinity Property:

\frac{c}{- \infty} = 0

= 0

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