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.`

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

Find the value of lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

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

Draw the graph of the function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(x^(2)-1) .

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then

Discuss the continuity of f(x)=("lim")_(nvecoo)cos^(2n)xdot