Answer
The Limit Does Not Exist.
Work Step by Step
As $t$ approaches 0, $\frac{1}{t}$ tends to $±\infty$.
However the $cos$ function is a non-constant periodic function, and $cos(x)$ takes values between $-1$ and $1$ for all $x∈ℝ$.
This means that when $\frac{1}{t}$ tends to infinity, $cos(x)$ doesn't tend to a specific value, but it rather could be anything between $-1$ and $1$.
Thus the given limit cannot exist.
