Limits at a Glance - Problem 1

Let's find some limits of rational functions using our tricks. Now the limit is x approaches infinity of 25x over x² plus 9. Just because the denominator has degree bigger than the numerator, you can automatically say that this limit is x approaches infinity is zero. Anytime the denominator has a bigger degree than the numerator this happens.

Now here the limit is x approaches infinity of 25x² over x² plus 9, because the degree are the same, we look at the leading coefficients 25 and just a marginal 1 in front of the x² and this limit becomes 25 over 1 or 25.

Now this is the harder case, the degree of the numerator is bigger than the degree of the denominator 25x³ over x² plus 9. This will go to either plus infinity or minus infinity, so which is it? Well as x goes to plus infinity, you can imagine that this term is always going to be positive and this term will be positive, so if the numerator and the denominator are both positive, this has got to go to positive infinity, there's no way it can go to negative infinity so it goes to positive infinity and that's it.