Consider `f(x) = lim_(x-oo)(x^n-sinx^n)/(x^n+sinx^n)`for`x>0,x!=1,f(1)=0` then

Let f(x)= lim_(n->oo)(sinx)^(2n)

lim_(x->oo)(1-x+x.e^(1/n))^n

f(x)=(lim)_(n->oo)(sin(pix/2))^(2n) for x >0,x!=1 ,and f(1)=0. Discuss the continuity at x=1.

The value of lim_(x->oo)(1+1/x^n)^x,n>0 is

Let f(x) = int_(0)^(pi)(sinx)^(n) dx, n in N then

Let f(x)=lim_(n->oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n)) . then

Evaluate lim_(x to oo) (sinx^(0))/(x).

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

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

If lim_(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to (a) 4 (b) 1 (c) 2 (d) 3