Thread: Can someone explain why this is?

Can someone explain why the limit of the function 1/sin²x is ∞ as x approaches 0(from both left and right).

I'm just starting to learn this, so as simple an explanation as you can manage would be appreciated.

What does the graph of 1/sin² x look like?

Since This means we can make as close to zero as we wish by making sufficiently close to . Thus we can make as large as we wish by making sufficiently close to .

We can be a little more precise with a definition if you wish.

Originally Posted by ImaCowOK

...What does the graph of 1/sin² x look like?

you can download this free graphing software form this site ...

Graph

... which can produce the graph of

Thanks, it makes a lot more sense now.

Note that for x= 0.001, sin(x)= 0.00001745329, approximately, so that [tex]sin^2(x)= 0.000000000304617419755778[tex] and then .

Of course, if x= -0.001, sin(x)= -0.0000174329 and so and are exactly the same as above.

Yes, I already understand that a negative number squared becomes positive.