`f(x)=(x^n-1)/(x-1) , x!=1` and `f(x)=n^2 , x=1` continuous at `x=1` then the value of `n`

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 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 to oo) (x^(2n-1) + ax^2 +bx)/(x^(2n) +1) . If f is continuous for x in R , then the value of a+8b is

f(x)={(1-x^n)/(1-x),\ \ \( x!=1, (n-1) at x=1, n in N at x=1

Let f(x)=(e^(x)-1)^(2n)/(sin^n (x//a)(log (1+(x//a)))^n for x ne 0 . If f(0)=16^n and f is a continuous function, then the value of a is

f(x)={(1-x^(n))/(1-x),quad x!=1n-1,quad x=1quad n in N at x=1

Let f(x) = (x - 1)(x - 2)(x - 3)…(x -n), n in N and f(')(n) = 5040 . Then the value of n is …..

Is the function f(X) = {:{((1-x^n)/(1-x), x ne 1),(n-1,x=1):} , n in N continuous at x =1?

For x in R, x != 0, x != 1 , let f_(0)(x)= (1)/(1-x) and f_(n+1)(x)=f_(0)(f_(n)(x)), n = 0, 1, 2,.... Then the value of f_(100)(3)+f_(1)(2/3)+f_(2)(3/2) is equal to