i think you meant that the other way around

other than that, the post is good. you neglected to mention how the signs affect the limit, but the examples you chose shows how to deal with them, so good job

looking forward to the next segment

i would also mention that neglecting the lower powers of x can work in a variety of environments, for example, under square roots and such.

for instance:

$\displaystyle \lim_{x \to \infty} \frac {3x}{\sqrt{4x^2 + 1}}$

we could treat this as $\displaystyle \lim_{x \to \infty} \frac {3x}{\sqrt{4x^2}} = \lim_{x \to \infty} \frac {3x}{2|x|} = \lim_{x \to \infty} \frac {3x}{2x} = \frac 32$

but be careful with this. sometimes dropping lower powers of x can come back to bite you. i saw a question like this the other day, i don't remember it now