Question Number 10137 by malwaan last updated on 26/Jan/17

lim_(x→0^+ )  ((sin x^m )/(sin^n  x))  n;m ∈Z

Answered by mrW1 last updated on 26/Jan/17

lim_(x→0^+ )  ((sin x^m )/(sin^n  x))  =lim_(x→0^+ )  (((sin x^m )/x^m )/((((sin x)/x))^n ))×x^(m−n)   =lim_(x→0^+ )  x^(m−n)   = { ((0, when m>n)),((1, when m=n)),((+∞, when m<n)) :}

Commented bymalwaan last updated on 27/Jan/17

what if x→0^(− )  or  x→0

Commented bymrW1 last updated on 27/Jan/17

the result should be the same.