What is $lim_(xrarr0+)(ln x) / (csc x)$ ?

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Answer 1 · 2015-12-09T16:45:25

It is $0$ .

The initial form is indeterminate $-oo/oo$ .

Apply l'Hopital's rule to get

$lim_(xrarr0^+) (1/x)/(-cscxcotx)$

Use trigonometry to rewrite this as

$lim_(xrarr0^+)(sinx/x * sinx/cosx)$

$= 1 * 0/1 = 0$

What is lim_(xrarr0+)(ln x) / (csc x)lim_(xrarr0+)(ln x) / (csc x)?