Question

Given `f(x) = sint/t`. How do you show that `f(t)` has a maximum value as `t->0`?

Answer 1

`f(t)` has a maximum value of 1 as `t->0`

Explanation:

`f(x) = sint/t`

Consider:
`lim_"t->0" f(t) = 1` [Standard limit]

Also consider:
Since `-1<=sint<=1 forall t in RR ->` any value of `abs(t)>0` will result in `f(x) <1`

Hence: `f(t)` has a maximum value of 1 as `t->0`