What is the limit as x approaches zero of f(x)=sin(1/x) ? Why would it be zero as opposed to undefined?

Question

anonymous · Answer

It is undefined...

cwrw238 · Answer

i think its is undefended

cwrw238 · Answer

* undefined  lol

anonymous · Answer

You can prove that the limit is undefined by the following method:

Make the following substitution for $\bf x$:$$\bf h=\frac{1}{x}$$Now as $\bf x$ approaches 0, $\bf h$ approaches $\bf  \infty$. Hence we re-write our limit  as:$$\bf \lim_{h \rightarrow \infty}\sin(h)=Undefined$$

anonymous · Answer

Ok thanks guys that's what i originally thought. My key must be wrong.

anonymous · Answer

By undefined it is implied that we can't really say what the limit will be because sine will keep bouncing around in the interval [0, 1] as h goes to infinity and won't really "approach" or "converge" to a specific value.

anonymous · Answer

And lol at your undefended @cwrw238