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University of California, Berkeley

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Problem 36

Finding a $\delta$ for a Given $\varepsilon$ The graph of

$f(x)=\frac{1}{x-1}$

is shown in the figure. Find $\delta$ such that if $0<|x-2|<\delta$ then $|f(x)-1|<0.01$

Answer

$\delta=\frac{1}{101}$

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## Discussion

## Video Transcript

okay from this from the Graf Spee feet out up to is equal to one. So the function might the limits. One is less than zero point there. One which means at one point there one lesson. Actually, that's the wrong way. Could be no 0.99 left in the back. Just one point 1.1. Okay. From the figure we see that effort Valley did that to you? Their one over 101 Is he going to 1.1? And this is all we waited at 199 over 99.99 So when ex doctor value of X minus two is last in Delta, that's that for a function minus the limit. Is that the 0.1? It gives us that to a one over 101 in less than X. What? You left in 199 over 99. Therefore, our delta is equal to the minimum of two. When it's to their one older one over one or a 9199 over 99 2 And the minimum is one over one on one