(4) `lim_(x rarr oo)(x+e^(x)+e^(2x))^((1)/(x))=e^(2)`

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

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

lim_(xrarr oo) (int_(0) ^(2x)xe^(x^(2))dx)/(e^(4x^2))

lim_(xrarroo) [x-log_(e)((e^(x)+e^(-x))/(2))]=

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

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

lim_(x rarr0)((a^(x)-1)/(x))=log_(e)a

lim_(x rarr0)(5^(x^(4))-1-x^(4)log_(e)5)/(x^(4))

lim_(x->oo)(e^(11x)-7x)^(1/(3x))

If 3x+2y=1 is a tangent to y=f(x) at x=1//2 , then lim_(xrarr0) (x(x-1))/(f((e^(2x))/(2))-f((e^(-2x))/(2)))