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

lim_(x->oo)(1-x+x.e^(1/n))^n

Let f(x)=(1-x)^(2)sin^(2)x+x^(2) for all x in IR, and let g(x)=int_(1)^(x)((2(t-1))/(t-1)-ln t)f(t) dt for all x,in(1,oo). Which of the following is true?

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Which of the following is true?

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the value of x.

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the range of x.

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the value of x.

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