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

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Answer 1 · 2017-03-10T08:36:09

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

$f(x) = sint/t$

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 $t->0$

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