limit_(n rarr oo)int_(0)^(2)(1+(t)/(n+1))^(n)dt" is "

lim_ (n rarr oo) int_ (0) ^ (2) (1+ (t) / (n + 1)) ^ (n) d

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

lim_(n rarr oo)((-1)^(n)n)/(n+1)

Let I_(n)=lim_(x rarr oo)int_(e-x)^(1)(ln(1)/(t))^(n)dt(n=1,2,3,...) then which of the following is(are) INCORRECT?

Calculate the reciprocal of the limit lim_(x rarr oo)int_(0)^(x)xe^(t^(2)-x^(2))dt

If Lt_(n rarr oo)int_(0)^(sqrt(a))(1-(x^(2))/(n))^(n)xdx=(1)/(2sqrt(2))(n in N) then the value of 'a' equals (n in N)

lim_(n rarr oo)(2^(n)+3^(n))^(1/n)

Assuming that the interchange of limit and integration is permissible,the value of lim_(n rarr oo)int_(0)^(1)(nx^(n-1))/(1+x)dx;^(@)0

lim_(n rarr oo)((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is

lim_(n rarr oo)(n)/(2^(n))int_(0)^(2)x^(n)dx equals