The Great Paradox of Limits

We say \lim_{x\rightarrow 2}x^{2}=4.

Let the limit be L .

So is L=4 or L<4 or L> 4 ?

Having addressed this question, can we conclude on the following statements:

1) \lim_{x\rightarrow 0}\frac{\sin x}{x}=1 \Rightarrow \sin x = x \Rightarrow \lim_{x\rightarrow 0}\frac{x}{x}=1

2) \lim_{x\rightarrow 0}\frac{\ln (1+x)}{x}=1 \Rightarrow \ln (1+x) = x \Rightarrow \lim_{x\rightarrow 0}\frac{x}{x}=1

I'd hope some expert clears this confusion with some detailed explaination!