`lim_(x->oo)x(a r c t a n(x+1)/(x+2)-a r c t a n x/(x+2))` is equal to

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

Let f : R toR " be a real function. The function "f" is double differentiable. If there exists "ninN" and "p inR" such that "lim_(xto oo)x^(n)f(x)=p" and there exists "lim_(x to oo)x^(n+1)f(x), "then" lim_(x to oo) x^(n+2)f''(x) is equal to

Let f : R toR " be a real function. The function "f" is double differentiable. If there exists "ninN" and "p inR" such that "lim_(x to oo)x^(n)f(x)=p" and there exists "lim_(x to oo)x^(n+1)f(x), "then" lim_(x to oo)x^(n+1)f'(x) is equal to

lim_(x->oo)((1^(1/x) +2^(1/x) +3^(1/x) +...+n^(1/x))/n)^(nx) is equal to

lim_ (n rarr oo) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))). ... + (1) / (2 ^ (n)) tan ((x) / (2 ^ (n))) is equal to lim_ (n rarr oo) sum_ (n = 1) ^ (n) (1 ) / (2 ^ (n)) tan ((x) / (2 ^ (n)))

lim_(x to oo ) tan { sum_(r=1)^(n) tan^(-1) ((1)/( 1 +r +r^2))} is equal to ________.

lim_(x rarr oo)n^(2)(x^((1)/(n))-x^((1)/((n+1)))),x>0, is equal to (a)0(b)e^(x)(c)(log)_(e)x(d) none of these

lim_(x->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x (c) (log)_e x (d) none of these