**Question:**

*True/False?*

$$ \lim_{x\to 0} \frac{sin(x^2)}{x^2}sin(\frac{1}{x}) = 1$$

**Discussion:**

As \(x\) goes to zero, \(x^2\) also goes to zero, and consequently, since $$ \lim_{y\to 0} \frac{sin(y)}{y}=1 $$ we have $$ \lim_{x\to 0} \frac{sin(x^2)}{x^2}= 1$$. If the statement were true, then \(\lim_{x\to 0}sin(\frac{1}{x}) = 1\), which is false. In fact, \(\lim_{x\to 0}sin(\frac{1}{x}) \) does not exist.

So the statement is **False. **

*Related*