If `f(x)=li m_(n->oo)(1+x)^n` comment on the continuity of `f(x) at x=0` and explain `lim_(x->0) (1+x)^(1/x) =e.`

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

Discuss the continuity of f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n+1))

Discuss the continuity of f(x)=(lim)_(n->oo)(x^(2n)-1)/(x^(2n)+1)

Discuss the continuity of f(x)=(lim)_(n->oo)(x^(2n)-1)/(x^(2n)+1)

If f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1) then range of f(x) is

f(x)=e^x then lim_(x rarr 0) f(f(x))^(1/{f(x)} is

lim_(n rarr oo)(1)/(1+n sin^(2)x), then find f((pi)/(4)) and also comment on the continuity at x=0

If f(x) = lim_(n->oo) tan^(-1) (4n^2(1-cos(x/n))) and g(x) = lim_(n->oo) n^2/2 ln cos(2x/n) then lim_(x->0) (e^(-2g(x)) -e^(f(x)))/(x^6) equals

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1) then for x>0,y>0,f(xy) is equal to