Indeterminate Forms

**Skyrim** · October 15th 2010, 07:08 PM

I know that 0*∞ is an indeterminate form. Is this provable?

**HallsofIvy** · October 16th 2010, 04:50 AM

What is yourdefinition of "indefinite form"?

I suspect you mean that you can have functions f(x), g(x), f'(x), and g'(x) such that $\lim_{x\to a} f(x)= 0$ . $\lim_{x\to a} g(x)= \infty$ , $\lim_{x\to a} f'(x)= 0$ , and $\lim_{x\to a} g'(x)= \infty$ such that $\lim_{x\to a} f(x)g(x)$ and $\lim_{x\to a} f'(x)g'= 0$ converge to different limits.

And you can prove that by showing such functions.

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