Lef `f(x) = lim_(x->0) (x^(2n) sin^n x)/(x^(2n)-sin^(2n) x) ,x != 0 and f(0)=L` for some n. If `f(x)` is continuous at `x = 0`, then

consider f(x)=lim_(x-oo)(x^(n)-sin x^(n))/(x^(n)+sin x^(n)) for x>0,x!=1,f(1)=0 then

Let f(x)=lim_(n rarr oo)(log(2+x)-x^(2n)sin x)/(1+x^(2n)) then

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.

Let f(x)=lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2 cos x)^(2n)), n in Z . Then

Let f(x)=lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2 cos x)^(2n)), n in Z . Then

(2) lim_(n rarr0) (n!sin x)/(n)

If lim_(x to 0) (x^n-sin^n x)/(x-sin^n x) is nonzero and finite , then n in equal to

Let f(x)=(lim)_(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)_(x->-oo)f(x)

A function f(x) is defined as f(x)=[x^(m)(sin1)/(x),x!=0,m in N and 0, if x=0 The least value of m for which f'(x) is continuous at x=0 is