Why Did the Negative Sign Disappear in the Calculus Example?

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kLPantera
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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
 

FAQ: Why Did the Negative Sign Disappear in the Calculus Example?

"Why does a negative number become positive when multiplied by another negative number?"

When multiplying two numbers with different signs, the result will always be negative. However, when multiplying two negative numbers, the two negative signs cancel each other out, resulting in a positive number.

"Why does a negative number disappear when added to a positive number?"

When adding two numbers with different signs, the result will depend on which number has a larger absolute value. When the positive number has a larger absolute value, the result will be positive. When the negative number has a larger absolute value, the result will be negative. However, when adding a negative number to a positive number, the negative sign is essentially subtracting the negative value from the positive value, resulting in a larger positive value and the disappearance of the negative sign.

"Why does a negative number become positive when divided by a negative number?"

Similar to multiplication, when dividing two numbers with different signs, the result will always be negative. However, when dividing a negative number by another negative number, the two negative signs cancel each other out, resulting in a positive number.

"Why does a negative number become positive when raised to an even power?"

When raising a number to an even power, the negative sign is essentially being multiplied by itself an even number of times. This means that the negative sign will be cancelled out, resulting in a positive number.

"Why does a negative number become negative when raised to an odd power?"

In contrast to the previous question, when raising a number to an odd power, the negative sign will not be cancelled out. This is because the negative sign is being multiplied by itself an odd number of times, resulting in a negative number.

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