if f(x)=<g(x) for all x not equal to c, then lim x->c f(x)=< lim x->c g(x). true or false? proof?

Question

I think the statement is true, but don't know how to proof it.

Answer 1

True. Informally, this is because the limit of a function does not depend on the value of the function at that point, only the values "near" the point, which are included in "all x not equal to c."

Answer 2

true provided f(c) & g(c) exists.