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.

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

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

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.

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.

If f(x)=lim_(nrarroo)((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n)) and lim_(xrarrpm1)f(x) exists, then The value of b is

If f(x)=lim_(nrarroo) ((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n)) and lim_(xrarrpm1) f(x) exists, then The value of a is

Let function f be defined as f:R^(+)toR^(+) and function g is defined as g:R^(+)toR^(+) . Functions f and g are continuous in their domain. Suppose, the function h(x)=lim_(ntooo)(x^(n)f(x)+x^(2))/(x^(n)+g(x)), x gt0 . If h(x) is continuous in its domain,then f(1).g(1) is equal to (a) 2 (b) 1 (c) 1/2 (d) 0

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_(ntooo) (x)/(x^(2n)+1). Then f has

Let f(x)=(lim)_(n rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.