Left and Right-Handed Limits

[Guest]

I found two tough questions. I need some tips.

READY?

1. Find the lim [(1/(x-1) - (1/|x-1|)] as x-->1 from the left.

2. Find the lim (x^2+x-6)/(x-2) as x-->2 from the right.

 

[galactus]

#1:

\(\displaystyle \L\\\lim_{x\to\1^{-}}\;\ \left(\frac{1}{x-1}\right)\;\ -\;\ \lim_{x\to\1^{-}}\;\ \left(\frac{1}{-(x-1)}\right)\)


#2:

\(\displaystyle \L\\\lim_{x\to\2^{+}}\frac{x^{2}+x-6}{x-2}=\lim_{x\to\2^{+}}\frac{(x-2)(x+3)}{x-2}\)

 

[Guest]

ok

Thanks for the tips.