Why Did the Negative Sign Disappear in the Calculus Example?

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The discussion addresses a specific calculus example regarding the disappearance of a negative sign during the simplification of the expression (x^2 - 3x) - x^2. The transition from (x^2 - 3x) - x^2 to 3x in the numerator is clarified as a correct simplification, where the negative sign is accounted for in the overall expression. Participants emphasize that the limit must be less than or equal to zero, confirming that the negative sign does not affect the final outcome of the limit calculation.

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http://math.colorado.edu/~jkeller/math1300/lectures/L8limits3.pdf

Example 8, the 2nd to 3rd step... where did the negative go? It's (x^2 - 3x) - x^2 then it became 3x in the numerator. Where'd the negative go? I don't see any other sign changes so could someone please tell me?
 
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It looks like an error: the minus sign should not have gone away. Intuitively, you can see the answer must be <= 0 because sqrt(x^2 - 3x) < x for x > 0, so when we subtract x we get a negative result. That does not allow for a positive limit.

RGV
 

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