Question

lim of cos^2(x)/x as x approaches -infinity

Answer 1

Since
\[cos^2(x) \]
is definitely going to remain finite

\[\frac{cos^2(x)}{x}\]

it going to hit 0 because any finite number divided by infinity is goin to be 0.

Now to actually show this, I would recommend something like squeeze theorem.
A delta epsilon proof would be pretty tricky.

Answer 2

so basically 0/x<=cos^2(x)/x<=1/x

Answer 3

Good job! Actually I wasn't sure which functions to use, but those functions definitely should work!

Answer 4

so would lim(x approches infinity) (sqrt(x^2+1))/(2x+1) be DNE since it would basically be infinity/infinity?