Find the values of `a` if `f(x)=("lim")_(n rarr oo)(a x^(2n)+2)/(x^(2n)+a+1)` is continuous at `x=1.`

lim_(n rarr oo)2^(1/n)

lim_(x rarr oo)((log x)/(x^(n)))

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

Evaluate: ("lim")_(n rarr oo)[(n !)/(n^n)]^(1//n)

lim_(x rarr oo)(log x^(n)-[x])/([x]),n in N,quad

Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim_( n to oo) (f(x)+x^(2n)g(x))/(1+x^(2n)) If F(x) is continuous at x=-1, then

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

f(x) = lim_(n rarr oo) ((x-1)^(2n) - 1)/((x-1)^(2n) + 1) is discontinuous at (A) x=0 only (B) x=2 only (C) x=0 and 2 (D) none of these

Let f(x)=lim_(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is continuous for all x in R then find the values of a and b.

A function f: RvecR is defined as f(x)=(lim)_(nvecoo)(a x^2+b x+c+e^(n x))/(1+c.e^(n x)) is continuous on R then find the values of a,b,c.