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University of California, Berkeley

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Problem 35

Finding a $\delta$ for a Given $\varepsilon$ The graph of $f(x)=x+1$ is shown in the figure. Find $\delta$ such that if $0<|x-2|<\delta$ , then $|f(x)-3|<0.4 .$

Answer

$\delta=.4$

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## Discussion

## Video Transcript

Okay, so we're given sl black and we need to find felt such that Jos, listen, actually, value backs money to is us on Delta. Then the function that's about all you have are function. My city is Listen, there is that our figure that's evaluated at two is equal to three. And we know that after all of effort, back when it's free lesson do important for oh, we have that 1.6 is in effect. Lesson 2.4 if we, um remover actually valid in and add three to both sides. Okay, uh, from the figure we feed at 1.6 is approximately 2.6 and evaluated at 2.43 point four. So we have that x minus to invest in Delta such that our function minus three doctor values of that is us and Joe 30.4. So this gives that 1.6 is less than X is less than 2.4. Therefore, delta is our minimum between two wonderful boys six and two point form. When it you, which is equal to point for. That means Delta is equal to 0.4