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Why don't these limits exist?

$$\lim_{x\to 0}\frac1{x^2}$$

Aren't we here just approaching $x$? And, thus will not get $0$ and avoid the division on "0"?

And, what about this limit?

$$\lim_{x\to 0}\frac{|x|}{x}$$

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    We are approaching x, but the value of 1/x tends to plus or minus infinity. (depends if you approach x=0 from below or above). 1/.001=1000, which is big.2011-03-21

4 Answers 4