- #1

- 2

- 0

f(x)=5x(x-2)(1/(x-2))

g(x)=5x(x-2)(1/(x-2)^2)

h(x) 5x(x-2)^2(1/(x-2)

The problem says that as x approaches 2, the functions take the form 0 times infinity, and asks you to "show" this. I tried plugging in 2 for x, but I got 0 times 1/0 (either undefined by 1/0 or indeterminate by 0/0) in each case. How am I supposed to get 0 times infinity?

The next part of the problem asks for the limits as x approaches 2, which I can see are 10, infinity (magnitude increasing without bound) and 0, respectively. The part after that says "Describe three things that the indeterminate form 0 times infinity could approach." Does that refer to the limits I just found, or some mathy smart thing I don't know about?

Your help would be much appreciated! Thanks!