Question

How could you find the solution for a limit if after applying direct substitution you get 0/infinity?

Answer 1

I don't believe this is an indeterminate form now that I've had more time to think about it.\[\large\rm \lim_{x\to a}\frac{f(x)}{g(x)}\]We were talking about the situation where f(a)=0 and g(x) is exploding up at x=a. (f and g continuous). So then we can think of our limit expression like this:\[\large\rm \lim_{x\to a}f(x)\cdot\frac{1}{g(x)}\]Which is approaching the form\[\large\rm 0\cdot\frac{1}{\infty}\]Which is really approaching\[\large\rm 0\cdot 0\]which is\[\large\rm 0\]

Answer 2

Oh this makes sense :)