calculating the limit

**bcahmel** · December 13th 2010, 12:42 PM

Problem: lim x--> infinity, w $x^{4/3}+4x^{1/3}$ all divided by $x^{5/4} -2x$ .(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 $x^{1/12}+4x^{-11/12}$ divided by $1-2x^{-1/4}$ .

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

**adkinsjr** · December 13th 2010, 01:54 PM

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

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

**Prove It** · December 13th 2010, 03:58 PM

Originally Posted by bcahmel

Problem: lim x--> infinity, w $x^{4/3}+4x^{1/3}$ all divided by $x^{5/4} -2x$ .(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 $x^{1/12}+4x^{-11/12}$ divided by $1-2x^{-1/4}$ .

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...

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

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

**bcahmel** · December 14th 2010, 11:36 AM

thank you both very much!

Thread: calculating the limit

LinkBack

Thread Tools

Display

calculating the limit

Similar Math Help Forum Discussions

calculating a limit

Calculating a Limit

Calculating limit

Need help Calculating the limit?

need help on calculating a limit.

Search Tags