Can somebody please answer this question for me please?

Recall the definitions of the asymptotic notations. We will say that f(x) has "order of growth x as xx0 " (where x0 is either some fixed real number or ) if f(x)=(x) as xx0. 1. Consider the functions f(x)=xsinx and g(x)=x. Is f(x)=(g(x)) as x ? Why or why not? (Hint: As always, you should refer back carefully to the definition of ().) 2. Suppose that we know that f(x)=x+(x2) and g(x)=(x)>0 as x0. Determine the order of growth of f(x)+g(x). (This problem is meant to get you comfortable with manipulating asymptotic notation when it appears in expressions. When I say something like " f(x)=x+(x2) ", this means that there is some function h(x)=(x2), and f(x)=x+h(x). That is, the fact that h(x)=(x2) is the only thing you know about h(x).) 3. Suppose that we know that f(x)=e(x) as x. Does this imply that f(x)=(ex) ? (Hint: Think carefully about the definition of (), and consider f(x)=e2x.)