Recent content by Lepros

If f(x) is in theta of h(x) and g(x) is in theta of h(x), then is f(x)+g(x) in theta of h(x)? My initial thoughts on this are yes since the addition of the two functions shouldn't impact the value of the largest degree in both functions, as they would if they were multiplied, but I'm wondering...

If f(x) if big-theta of g(x), is it also always the case then that g(x) is big-theta of f(x)?

I have the following limit problem: $$\Large\lim_{x \rightarrow \infty}\frac{x^{\frac{5}{3}}}{e^{2x}}$$ I have reduced it to the following using L'Hôpital's rule once and basic algebra: $$\Large\lim_{x \rightarrow \infty}\frac{5}{2e^{2x}3x^{\frac{-2}{3}}}$$ I can tell that the limit is 0, but...