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University of California, Berkeley

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Problem 19

Limits That Fail to Exist In Exercises 19 and 20 , create a table of values for the function and use the result to explain why the limit does not exist.

$$\lim _{x \rightarrow 0} \frac{2}{x^{3}}$$

Answer

See step for solution

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## Discussion

## Video Transcript

Okay, so we're back to create a stable. So it's blood includes the legal point one and then if we plug it into our function, function is equal. Feeling the 10 to the power of three. Perfect vehicle to negative 0.1 Our assumption end Then they tend to fire. Six of X is equal to negative points. The other one our function is equal to you Don't tend to hurt. Well, it's $2 to my right hand side. So what gives Excellent too. They're all points. So they're one. Our function is equal to 10 3 bars. Night Simitis, as X approaches zero from our left hand side with Your deeds are always here. Our function is approaching negative infinity. But as X approaches, they're all from the right hand side, which is this fellow here we get 10 to the power line, but that is a really large numbers. This queen just approaching infinity and, uh, we're increasing without abound as X approaches from the right and left or limit is not this because we're approaching two different values and they're both going off to negative infinity and infinity

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