hi, im unsure on how to solve a certain limit using the sandwhich rule.
lim [(x-3) sin(1/(3-x))] as x -> 3
any help or hints would be much appreciated..thank you
The limit can be re-written as
$\displaystyle \lim_{y \rightarrow 0} (-y) \, \sin\left( \frac{1}{y} \right) = -\lim_{y \rightarrow 0}y \, \sin\left( \frac{1}{y} \right)$
where y = 3 - x.
This in turn can be re-writen as $\displaystyle - \lim_{t \rightarrow \infty} \frac{\sin t}{t}$
where $\displaystyle t = \frac{1}{y}$.
Now read this.