M Meddle New member Joined Jun 2, 2010 Messages 1 Jun 2, 2010 #1 Hi guys, I have some problems proving Epsilon-Delta as x approaches infinity questions. Here's the one: lim x->infinity (x^2 - 2x) / (x^3 -5) = 0 How do I pick N? I'm totally confused now with the ones are proved with delta.
Hi guys, I have some problems proving Epsilon-Delta as x approaches infinity questions. Here's the one: lim x->infinity (x^2 - 2x) / (x^3 -5) = 0 How do I pick N? I'm totally confused now with the ones are proved with delta.
B BigGlenntheHeavy Senior Member Joined Mar 8, 2009 Messages 1,577 Jun 3, 2010 #2 \(\displaystyle Note: \ \lim_{x\to\infty}\frac{x^2-2x}{x^3-5} \ = \ \lim_{x\to\infty}\frac{x^2}{x^3} \ = \ \lim_{x\to\infty}\frac{1}{x} \ = \ 0\) \(\displaystyle Now, \ can \ you \ take \ it \ from \ here?\)
\(\displaystyle Note: \ \lim_{x\to\infty}\frac{x^2-2x}{x^3-5} \ = \ \lim_{x\to\infty}\frac{x^2}{x^3} \ = \ \lim_{x\to\infty}\frac{1}{x} \ = \ 0\) \(\displaystyle Now, \ can \ you \ take \ it \ from \ here?\)
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Jun 3, 2010 #3 Here is a 'made up' example close to yours I will use as an example. \(\displaystyle \lim_{x\to {\infty}}\frac{1}{x-1}=0\) \(\displaystyle x>N\) \(\displaystyle N=\frac{1+{\epsilon}}{\epsilon}=1+\frac{1}{\epsilon}\) \(\displaystyle x>\frac{1}{\epsilon}+1\) \(\displaystyle x-1>\frac{1}{\epsilon}\) \(\displaystyle \frac{1}{x-1}<{\epsilon}\) Now, close it up?.
Here is a 'made up' example close to yours I will use as an example. \(\displaystyle \lim_{x\to {\infty}}\frac{1}{x-1}=0\) \(\displaystyle x>N\) \(\displaystyle N=\frac{1+{\epsilon}}{\epsilon}=1+\frac{1}{\epsilon}\) \(\displaystyle x>\frac{1}{\epsilon}+1\) \(\displaystyle x-1>\frac{1}{\epsilon}\) \(\displaystyle \frac{1}{x-1}<{\epsilon}\) Now, close it up?.
