Discuss the continuity of `f(x)=("lim")_(n->oo)cos^(2n)xdot`

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

lim_(n->oo) nsin(1/n)

Discuss continuity of function f(x)=1+ lim_(n to oo) cos^(2n) x. Draw the graph of the function and find the period of the function .

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

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

Discuss the continuity of f(x)in[0,2],w h e r ef(x)=(lim)_(n->oo)(sin (pix/2))^(2n)

Find the number of integers lying in the interval (0,4) where the function f(x)=(lim)_(n->oo)(cos( pix/2))^(2n) is discontinuous

lim_(n->oo)sin(x/2^n)/(x/2^n)

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

Let y_(n)(x) = x^(2) + (x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+......(x^(2))/((1+x^(2))^(n-1))and y(x) = lim_(n rarr oo) y_(n) (x) . Discuss the continuity of y_(n)(x)(n = 1, 2, 3....n) and y(x) "at x" = 0