What is the limit (calculus II)

What is the limit as n approaches infinity of n^(1/2)/(2*n^(1/2)+n^(1/3)) and what were your steps to getting the answer?

Divide by n^(1/2) and you will see that the limit is 1/2

If we divide the numerator and denominator by √n, the term with the highest power, we get:
lim (n-->infinity) √n/[2√n + n^(1/3)] = lim (n-->infinity) (√n/√n)/{[2√n + n^(1/3)]/√n}
= lim (n-->infinity) 1/[2√n/√n + n^(1/3)/√n]
= lim (n-->infinity) 1/[2 + n^(1/3 - 1/2)], by the laws of exponents
= lim (n-->infinity) 1/[2 + n^(-1/6)].

Since n^(-1/6) --> 0 as n --> infinity, we see that:
lim (n-->infinity) 1/[2 + n^(-1/6)] = 1/(2 + 0) = 1/2.

I hope this helps