simple question on limit

ratios

Hello all,

I don't understand why |h|/h will become -1 as h approches 0 from the left. I can see how the numerator becomes negative, as |x| = -x if x< 0, but shouldn't the denominator become negative also since h < 0 when we approach 0 from the left? So why isn't the answer -h/-h = 1?

StatusX

The numerator is always positive. It's true that |x|=-x when x<0, but in that case -x>0, and |x|/x=-x/x=-1.

Hurkyl

Quote by ratios

I can see how the numerator becomes negative, as |x| = -x if x< 0

You see wrong. Here, -x is positive.

ratios

Okay I see. Thanks for the help!

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ratios	simple question on limit Tweet Hello all, I don't understand why \|h\|/h will become -1 as h approches 0 from the left. I can see how the numerator becomes negative, as \|x\| = -x if x< 0, but shouldn't the denominator become negative also since h < 0 when we approach 0 from the left? So why isn't the answer -h/-h = 1?

StatusX Recognitions: Homework Help	The numerator is always positive. It's true that \|x\|=-x when x<0, but in that case -x>0, and \|x\|/x=-x/x=-1.

ratios	simple question on limit Okay I see. Thanks for the help!