Question

Please explain this!
http://i.imgur.com/zY2odhC.jpg

# 83 please. I know it's 0 but why? I thought if we plugged 0 into sin(1/x) then it would be undefined and then it wouldn't work anymore. :o

Answer 1

Squeeze Theorem.

Answer 2

More specifically,
\[-1\leq\sin\left(\frac{1}{x}\right)\leq1\\
\Rightarrow -x\leq x\sin\left(\frac{1}{x}\right)\leq x\]
SInce both -x and x approach 0 as x approaches 0, and x sin(1/x) is "squeezed" between these two, x sin(1/x) also approaches 0 as x approaches 0.