On Wed, 01 Jun 2011 10:45:17 -0700, Alexandros Bantis <firstname.lastname@example.org> wrote in <news:94nc5dFituU1@mid.individual.net> in alt.math.undergrad:
> I'm working on Salas (10th Ed) Calculus: One and Several Variables. > Problem #41
> "Define the function at 5 so that it becomes continuous at 5:
> f(x) = sqrt(x+4)-3 / (x-5)
I'm assuming that you mean [sqrt(x + 4) - 3] / (x - 5).
> I tried multiplying by (sqrt(x+4)+3)/(sqrt(x+4)+3), which > resulted in 1/(sqrt(x+4)-3)
Algebra error: that should be 1 / [sqrt(x + 4) + 3], so that the limit of f(x) as x approaches 5 is 1/6. To make f continuous at x = 5, therefore, its definition must be extended to x = 5 by setting f(5) = 1/6.
> which is still not continuous as x approaches 5.
Incorrect terminology: both what you had and the correct expression *are* continuous as x approaches 5. The difference is that one of them has a value at x = 5, and the other hasn't.