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Problem 72

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Problem 70

by evaluating $f$ at $x$ -values near $0 .$ Sketch the graph of $f$

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

Estimate

$\lim _{x \rightarrow 0} \frac{|x+1|-|x-1|}{x}$

by evaluating $f$ at $x$ -values near $0 .$ Sketch the graph of $f$

Answer

See step for solution

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## Discussion

## Video Transcript

we were given the following them as X approaches Arab, actually about the practice possible in nice. Absolute value explains one over X. So we're asked a favor us out in two different ways. So first of all, we can create a table unplugging different values of X were not approaches. Zero. So we want to choose numbers around. You're also scenarios. There points that one Buser appoints a rope. What was your point? One? They would drop my Seirawan ago. 0.1 It's a possibility, right? At 0.1 I mean, 0.1 no. 0.1. So these air Melo surrounding from zero and so just simple progress and your equation. We should get to every single time. And so this is the area where Vera would be and so we can face off with this. It seems to me that the limit as experts sterile dysfunction of X seems to be approaching two. Now, we can once again with your autograph, this to see if this matches up. So if we this is our graph and so we zoom in, we can see that as the function of purchase zero seems possibly approaching two. So based off of this, we can say that the limit as extras area of absolute value expose one marks actual value expired one over X is equal to two.

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