Find Delta

**dangbeau** · February 12th 2013, 09:20 PM

Hi guys, I really need help.
I'm stucking at this question, any suggestion? Can you explain how to solve it step by step?

f(x)= 1/(x-1)
Find the largest δ such that if 0 < |x – 2| < δ then |f(x) – 1| < 0.01

**Plato** · February 13th 2013, 03:50 AM

Originally Posted by dangbeau

Hi guys, I really need help.
I'm stucking at this question, any suggestion? Can you explain how to solve it step by step?
f(x)= 1/(x-1)
Find the largest δ such that if 0 < |x – 2| < δ then |f(x) – 1| < 0.01

This is not a tutorial service, therefore do not ask for a step-by-step solution.
You can pay a tutor for that. This is free.

Note that $|f(x)-1|=\left|\frac{x-2}{x-1}\right|$ .

If $0<\delta<1~\&~|x-2|<\delta$ then $-\delta<x-2<\delta$ or $1-\delta<x-1<\delta+1$ or $\left|\frac{x-2}{x-1}\right|=\frac{|x-2|}{|x-1|}< \frac{\delta}{1-\delta}$

**dangbeau** · February 13th 2013, 05:52 AM

Yay I got it now
you are my lifesaver, thank you so muchhhh

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