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University of California, Berkeley

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Problem 7

Estimating a Limit Numerically In Exercises $5-10$ , complete the table and use the result to

estimate the limit. Use a graphing utility to graph the function to confirm your result.

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

Answer

$$\lim _{x \rightarrow 0} \frac{\sqrt{x+1}-1}{x} \approx 0.5$$

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## Discussion

## Video Transcript

Okay, so at X is equal to negative 0.1. You have our function square root and then dyed 0.1, but one minus one over in the 0.1. And that gives us. Is there a 0.5123 when X is equal to native 0.1 where anything could go 0.1111 over Native girl point there once that gives a point or no 0.0.5012 that one. Actually platoon Ingrid still points No. One. Our function is good point her native points. So one plus one. Why this one all over Major plane goes. So what? Which gives us approximately 0.5. Okay, now when X is equal to no, our function is undefined because we're dividing by. So now, when X is equal to 0.1 spirit of 0.111 over at 0.1 gives me approximately 0.499 When Exit E puts the 0.1 get rid of Joe 0.1 +11 it's one over 10.1. He's approximately 1.498 and when exit equal to 0.1. This grapefruit of point go. Our 0.0.1, but one minus one over 10.1. The popular only point for a eight. Okay, now, looking at this table. Oh, um, what X approaches euro from the right were actually getting close to 2.5. And so is it from approaching or last night? So we can say that limit. What's one more corn? Well, the X is approximately zero point.