Patrick B. answered • 08/29/19
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x^2 - 7x + 12 = ( x - 4 )(x - 3 )
since the limit is approaching 3 from the left, we have x<3,
which means x-3<0.
We can drop the absolute value sign and replace it with 3-x, since it is negative.
This cancels with x-3 in the denominator but leaves as factor of -1.
the function simplifies to -1/(x-4)
the limit is then (-1)/(3-4) = (-1)/(-1) = 1
Cass G.
thank you! This helped so much!
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08/29/19
Patrick B.
The reason why the x-3 gets switched to 3-x is because it is inside the absolute value and is NEGATIVE. REcall, the definition of absolute value: |z| = z if z>0 is positive But |z| = -z if z<0 is negative Of course |z| = 0 if z=0 It is negative because x is approaching the 3 from the LEFT, which makes is negative. So then |x-3| = -(x-3) by definition = 3-x08/29/19