1. ## calculating the limit

Problem: lim x--> infinity, w $\displaystyle x^{4/3}+4x^{1/3}$ all divided by $\displaystyle x^{5/4} -2x$.(sry couldn't figure out how to make it into a fraction).

From there I divided the numerator and the denominator by x^(5/4), and I ended up with $\displaystyle x^{1/12}+4x^{-11/12}$ divided by $\displaystyle 1-2x^{-1/4}$.

I kind of confused on what I do from here to find the limit...Any help please?

2. You don't need to go through all this. When working with rational expressions like this, just use the highest powers.

$\displaystyle \lim_{x->\infty}\frac{x^{\frac{4}{3}}+4x^{\frac{1}{3}}}{x^ {\frac{5}{4}}-2x}=\lim_{x->\infty}\frac{x^{\frac{4}{3}}}{x^{\frac{5}{4}}}$

3. Originally Posted by bcahmel
Problem: lim x--> infinity, w $\displaystyle x^{4/3}+4x^{1/3}$ all divided by $\displaystyle x^{5/4} -2x$.(sry couldn't figure out how to make it into a fraction).

From there I divided the numerator and the denominator by x^(5/4), and I ended up with $\displaystyle x^{1/12}+4x^{-11/12}$ divided by $\displaystyle 1-2x^{-1/4}$.

I kind of confused on what I do from here to find the limit...Any help please?
What you are doing is correct, but it's easiest to write each term as its own fraction...

$\displaystyle \displaystyle \lim_{x \to \infty}\frac{x^{\frac{4}{3}} + 4x^{\frac{1}{3}}}{x^{\frac{5}{4}} - 2x} = \lim_{x \to \infty}\frac{x^{\frac{1}{12}} + \frac{4}{x^{\frac{11}{12}}}}{ 1 - \frac{2}{x^{\frac{1}{4}}}}$.

All the terms that have $\displaystyle \displaystyle x$ in the denominator go to $\displaystyle \displaystyle 0$, while the $\displaystyle \displaystyle x^{\frac{1}{12}}$ still goes to $\displaystyle \displaystyle \infty$. So the limit is $\displaystyle \displaystyle \infty$.

4. thank you both very much!