Evaluate $\lim_{t \to \infty} \frac{(\sqrt t+ t^2)}{(4t - t^2)}$. Why is the limit as $t \to \infty = 0$? Would like some feedback on my process. Also, would like to gain a Calculus I understanding of limits. 
A question many are having a problem explaining to me is why is the limit as x approaches infinity designated as zero. Thats is, when I get to the point of solving a limit expression or function, why is it as x approaches infinity the value is designated zero?
Surely the number can be a very high positive number also? Or am I missing something here? for example why is the limit as x approached infinity $1/x = o$? What if x is 0.0001?  

You have the right idea dividing through by the highest power, but something went a bit wrong after that... for one, what makes you so sure you can split limits up and take them separately over the numerator and denominator? You also had a mistake cancelling out your exponents - for example, the numerator in the upper-right corner should have reduced to $1/t^{3/2} + 1$. After that, in the denominator, you also have to distribute 1/t, not put it on only one of the two terms in the numerator.
