💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 45 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) $


$\lim _{x \rightarrow 0^{-}} \frac{2}{x}$ which doesn't exist since denominator approaches 0 and numerator doesn't. To clarify this limit would be equal to negative infinity, but since
infinity is not a limit it would therefore be considered as not existent i.e. D.N.E.

More Answers


You must be signed in to discuss.

Video Transcript

to evaluate this limit, we know that the absolute value of X this is equal to negative X. If Access less than zero and positive X if X is greater than zero. Now, since excess approaching zero from the left, then we're talking about absolute value of X equals negative X. And so in here we can write this as the limit As X approaches zero from the left of one over X one over negative x. Which you can simplify further into the limit As X approaches zero from the left of one over X plus one over X. Or this is the same as The limited sex approaches zero From the left of two over X Known that as X approaches zero from the left, the value of X is a very small negative number. So The value of two over X would be approaching negative infinity. And so this limit As X approaches zero from the left of two over X must be negative infinity.