f) `lim_(x rarr oo)(x)^(2/x)`

lim_(x rarr oo)e^(-x)x^(2)

lim_(x rarr0)(1+2x)^(5/x)

lim_(x rarr oo)(sqrt(x^(2)+x)-x)

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.

The value of lim_(a rarr oo)(1)/(a^(2))int_(0)^(a)ln(1+e^(x))dx equals

lim_(x rarr0)(2x^2-3x)/x

lim_(x rarr oo)((log x)/(x))^(1/x)

lim_(x rarr oo){((log x)^(3))/(x)}

lim_(x rarr oo)(log(1+x))/(x)

lim_(x rarr oo)(sqrt(x^(2)+x+1)-sqrt(x^(2)+1))