`lim_(x to 00)(x^(n)+a^(n))/(x^(n)-a^(n))=`________.

lim_(x rarr oo) (x^(n)+a^(n))/(x^(n)-a^(n))= ________.

Evaluate: lim_(x rarr a) [(x^(n)-a^(n))/(x^(m)-a^(m))] .

lim_(x to a) (x^(m)-a^(m))/(x^(n)-a^(n)) is equal to

lim_(x rarr a)(x^(m)-a^(m))/(x^(n)-a^(n))=((m)/(n))a^(m-n) if m>n

Letf(x) = lim_( n to oo) (x^(n)-sin x^(n))/(x^(n)+sin x^(n)) " for" xgt 0, x ne 1,and f(1)=0 Discuss the continuity at x=1.

The equivalent definition of the function f(x)=lim_(n to oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)), x gt 0 , is

The equivalent definition of the function f(x)=lim_(n to oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)), x gt 0 , is

(i) lim_(xrarra) (x^(m)-a^(m))/(x^(n)-a^(n)) (ii) lim_(xrarra) ((1+x)^(1//n)-1)/(x)

(i) lim_(xrarra) (x^(m)-a^(m))/(x^(n)-a^(n)) (ii) lim_(xrarra) ((1+x)^(1//n)-1)/(x)