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?

I think the statement is true, but don't know how to proof it.If f(x)=%26lt;g(x) for all x not equal to c, then lim x-%26gt;c f(x)=%26lt; lim x-%26gt;c g(x). true or false? proof?
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.';If f(x)=%26lt;g(x) for all x not equal to c, then lim x-%26gt;c f(x)=%26lt; lim x-%26gt;c g(x). true or false? proof?
true provided f(c) %26amp; g(c) exists.