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
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Note that $\displaystyle |f(x)-1|=\left|\frac{x-2}{x-1}\right|$.
If $\displaystyle 0<\delta<1~\&~|x-2|<\delta$ then $\displaystyle -\delta<x-2<\delta$ or $\displaystyle 1-\delta<x-1<\delta+1$ or $\displaystyle \left|\frac{x-2}{x-1}\right|=\frac{|x-2|}{|x-1|}< \frac{\delta}{1-\delta}$