Question

consider the function f(x)=sin(1/x)
how do you think the function behaves near x=0? Explain your reasoning

Answer 1

wiggles like crazy

Answer 2

It does but it would leave a hole a x=0 because the function has an asymptote there.

Answer 3

so how does it behave near 0?

Answer 4

https://www.desmos.com/calculator/2aluh6psem

Answer 5

how would i explain how the function behaves as it approaches 0? just that it curves a lot?

Answer 6

You can say that it wobble more as x get closer to 0.

http://www.math.washington.edu/~conroy/general/sin1overx/