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.