True or False: Limits

[courtneya10]

If lim as x approaches a of f(x) = L and lim as x approaches a of g(x) = L, then f(x) = g(x) for all values of x near a, except possibly at a. True or False

I thought this was false because if you had even just a positive and negative straight line that intersected at the same point they would not be equal, however now I am second guessing myself. Please help!

 

[Dr.Peterson]

Don't second-guess yourself too much. (After sensibly doubting your first thoughts, you should next doubt your doubts.)

You've given a nice, simple counterexample. Sounds convincing to me!