Calling all Calculus Whizzes

[Nixona]

I've got a prob that isn't necessarilly difficult, but deal more with concepts than real numbers and I just can't get it. I'll try to write it out as best I can.

Define f,g : R -> R be functions such that:
lim f(x) (as x approaches 0) = a a does not equal 0
lim g(x) (as x approaches 0) = 0

Prove that: lim (as x approaches 0) f(x)/g(x) cannot exist as a real number.

Then, let f:R->R be a function and b in the real number line such that f is NOT continuous a b. Use the previous problem to show that f is NOT differentiable at b.

Got all that?

The first part seemed rather simple...the limit (as x approaches 0) of f(x)/g(x)= a/0, where a does not equal 0. You cannot divide any real number by zero and obtain a real number. But beyond that...things are just out of grasp for me it seems. Any input would be appreciated while I sit here scratching my head. Thanks.

[ablang]

Geezaloo! Is this calculus or pre-calc? Either way, it's the part of it that I no longer remember how to do.

You might get the answer you seek on the Usenet newsgroups under sci.math

http://groups.google.com/groups?hl=e...group=sci.math