# How do you find lim cost/t^2 as t->oo?

May 10, 2017

$0$

#### Explanation:

$\cos t$ oscillates between the values of $- 1$ and $1$.

The denominator, ${t}^{2}$, approaches $\infty$ as $t \rightarrow \infty$.

It's fairly simple to see that no matter what the value of $\cos t$ is, it will be significantly "overpowered" by the growth of ${t}^{2}$ in the denominator.

As $t$ gets sufficiently large, we will have very large values in the denominator and only value between $- 1$ and $1$ in the numerator.

Thus, we get values like $\frac{1}{10000}$ and $- \frac{1}{100000000}$ as $t$ increases. These terms get closer and closer to being $0$.

So:

${\lim}_{t \rightarrow \infty} \cos \frac{t}{t} ^ 2 = 0$