- #1
ktpr2
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This pretty book here says that [tex] \lim_{x\rightarrow 0^-}\frac {|x|}{x} [/tex] is equal to [tex] \lim_{x\rightarrow 0^-}\frac {-x}{x} [/tex] ...
I understand that we're taking a left sided limit, as x approaches 0, so x will always be negative, but we're putting that value in the absolute value function which should always return a postive result. So what's the conceptual reason for the absolute value function returning a negative number? The only thing I could come up with is the order of operation application is different; you take the absolute value of x first and then let that x approach 0 from the left, which would be result in a negative x.
I understand that we're taking a left sided limit, as x approaches 0, so x will always be negative, but we're putting that value in the absolute value function which should always return a postive result. So what's the conceptual reason for the absolute value function returning a negative number? The only thing I could come up with is the order of operation application is different; you take the absolute value of x first and then let that x approach 0 from the left, which would be result in a negative x.
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