`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

If lim_(x->1)((x^n-1)/(n(x-1)))^(1/(x-1))=e^p , then p is equal to

lim_(x rarr oo)(1-x+x*e^((1)/(n)))^(n)

The value of lim_(x->oo)((2^(x^n))^(1/e^x)-(3^(x^n))^(1/e^x))/(x^n) (where n in N) is (a)logn(2/3) (b) 0 (c) nlogn(2/3) (d) none of defined

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1), then f or x>0,y>0,f(xy) is equal to : f(x)f(y) (b) f(x)+f(y)f(x)-f(y)(d) none of these

lim_ (n rarr oo) n ^ (2) (x ^ ((1) / (n)) - x ^ ((1) / (n + 1))), x> 0

lim_(x->oo)(e^x((2^(x^n))^(1/(e^(x)))-(3^(x^n))^(1/(e^(x)))))/(x^n), n in N, is equal to

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

lim_(x rarr oo){(1)/(1-n^(2))+(2)/(1-n^(2))+(n)/(1-n^(2))} is equal to 0 (b) -(1)/(2)(c)(1)/(2)(d) none of these

lim_(x rarr0)((1+tan x)/(1+sin x))^(csc x) is equal to e (b) (1)/(e)(c)1 (d) none of these