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Numerade Educator

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Problem 46 Easy Difficulty

Find the limit, if it exists. If the limit does not exist, explain why.

$ \displaystyle \lim_{x \to 0^+}\left(\frac{1}{x} - \frac{1}{|x|} \right) $

Answer

$\lim _{x \rightarrow 0^{+}}\left(\frac{1}{x}-\frac{1}{|x|}\right)=0$

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Video Transcript

is problem number forty six of this tour Tactless eighth edition section two point three Find the limited It exists. There's a limit does not exist. Explain away the limit is expert zero from the right of the quantity one over X minus one over the absolute value picks. We notice that as experts zero, each of these terms is indeterminant. So our approach is to combine the two factions and cft functions and defines in any way we haven't upset value function here. Ah, that we first I need to deal with before we can try to combine the two fractions on what we know about the absence of Value X is that it is the same as just a God you x are the function X when X is greater than or equal to zero and it's equivalent to negative X when X is less than zero for this limit, though, however, we are only concerned with ex approaching zero from the right. This guarantees that the values of X are positive and or equal to zero. And so our absolute value function reduces too absolutely of X rays to just x pretties for for the for the reason that we're putting serve from the right and that the function itself is just the same as X in this region. Now we can see that we can simplify this limit pretty easily. One over X minus on a rex gives us zero. And the limit is you're prettier from the right of dysfunction. Zero gives us the upper limit from the right is equal to zero.