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

Mar 10, 2017

$f \left(t\right)$ has a maximum value of 1 as $t \to 0$

Explanation:

$f \left(x\right) = \sin \frac{t}{t}$

Consider:
${\lim}_{\text{t->0}} f \left(t\right) = 1$ [Standard limit]

Also consider:
Since $- 1 \le \sin t \le 1 \forall t \in \mathbb{R} \to$ any value of $\left\mid t \right\mid > 0$ will result in $f \left(x\right) < 1$

Hence: $f \left(t\right)$ has a maximum value of 1 as $t \to 0$