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# Use the given graph of $f$ to find a number $\delta$ such thatif $0 < \left| x - 3 \right| < \delta$ then $\left| f(x) - 2 \right| < 0.5$

## 0.4

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

So in this problem were given this graph we're asked to find the number delta. Such that If zero is less than the absolute value of X -3, less than delta then F of x minus two sorry minus two is less than 0.5. Okay, so You can see from the graph right that when F of X -2 is less than .5? Well then we are in this range aren't we? Somewhere between 2.5 and 1.5 for the F of X. Okay. And that means then that We have these two deltas, right? Delta one Will be 3 -2.6 which is 0.4 and Delta two which will be 3.8 -3 which is me fix that up just a little bit right there because that's an absolute value sign there we go. 0.8. And so then that means that the delta we're looking for is the minimum Of these two Delta 1 and delta two. The minimum of those two is .4. So this is 0.4. So we noticed that If .4 is delta and everything less than .4 away from three, Right from 2.6 up to 3.4 being that range right there wouldn't It is all within 0.5 of two on the f. Of X, is it not? It is okay. Yeah so there's our answer. Um Right there

DM
Oklahoma State University

#### Topics

Limits

Derivatives

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp