Question

evaluate lim x → ∞ cos x 5 x

Answer 1

Do you mean \[\lim_{x\rightarrow \infty} \cos x\cdot 5x\]?

Answer 2

yes

Answer 3

<infinity

Answer 4

As cos x is bounded in [-1,1] you have
\[constant\cdot\infty\]
so it is infinty the result.