My Math Forum Find the largest Delta

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 February 12th, 2013, 04:17 PM #1 Newbie   Joined: Feb 2013 Posts: 1 Thanks: 0 Find the largest Delta How to solve this problem? can anyone help me I'll be very appreciated if it's explained step by step The graph of the following function is shown in the figure. Find the largest ? such that if 0 < |x – 2| < ? then |f(x) – 1| < 0.01. f(x) =1/( x ? 1) http://i.imgur.com/ZLvTR5h.png
 February 13th, 2013, 04:41 AM #2 Member   Joined: Jan 2013 Posts: 93 Thanks: 0 Re: Find the largest delta $\left|\frac{1}{x-1}-1\right|<\frac{1}{100}$ $\Leftrightarrow$ $-\frac{1}{100} < \frac{1}{x-1}-1 < \frac{1}{100}$ $\Leftrightarrow$ $\frac{99}{100} < \frac{1}{x-1} < \frac{101}{100}$ $\Leftrightarrow$ $\frac{100}{101} < x-1 < \frac{100}{99}$ $\Leftrightarrow$ $-\frac{1}{101} < x-2 < \frac{1}{99}$ Hence $\delta=\min\left\{\frac{1}{101}, \frac{1}{99}\right\}=\frac{1}{101}$.

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### the graph of f(x) = x 1 is shown in the figure. find the largest Î´ s.

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