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Calc. problem I don't understand?
suppose |x|<=2
use properties of absolute values to show that |(2x^2+3x+2)/(x^2+2)|<=8
<= is for less than or equal to
So, I understand all my other hw problems about solving inequalities, I just don't know what to do with this one. So if you could explain the steps I'd be very appreciative.
1 Answer
- dmoney_scLv 51 decade agoFavorite Answer
If |x| is <=2 then x is between -2 and 2. So x² is between 0 and 2.
The highest possible value for the numerator is almost 16 if x is almost +2. It can be as low as 2. The lowest possible value for the denominator is 2 when x=0, and it will be almost 6 when x is nearly 2. That means the fraction cannot possibly be more than 8 (16/2) and actually it will never be over about 2.7. You can even say that (2x²+3x+2) / (x²+2) <=8, because both the numerator and denominator will always be positive if |x|<=2.
