1. ## Continuous Limits

Hi everyone,

I am looking for help with the following problem:

Show that the function is continuous @ the given number 'a':

f(x) = x^2 + sqrt(7-x) a = 4

I am struggling with the entire topic of limits, so please be very deliberate about the steps and make your answer easy to digest... Thanks so much in advance!

2. Originally Posted by infinity257
Hi everyone,

I am looking for help with the following problem:

Show that the function is continuous @ the given number 'a':

f(x) = x^2 + sqrt(7-x) a = 4

I am struggling with the entire topic of limits, so please be very deliberate about the steps and make your answer easy to digest... Thanks so much in advance!
You are expected to prove that $\displaystyle \displaystyle \lim_{x \to 4} f(x) = f(4)$, that is, $\displaystyle \displaystyle \lim_{x \to 4} (x^2 + \sqrt{7 - x}) = 16 + \sqrt{3}$.

Since you seem to be just starting limits, you're probably expected to use basic 'algebra of limits' theorems and given limits of standard functions to do this.

(Although you might be required to do an epsilon-delta proof. But if you don't know what that is, then you probably aren't required to do it).

3. Ok, so I did get as far as 16 + sqrt(3) before coming on here... and I know how to get there, but is that as far as I can go / is that the final answer they are looking for?

Also, how do you guys make those fancy equation pictures... theyre so much easier to read!

4. Originally Posted by infinity257
Ok, so I did get as far as 16 + sqrt(3) before coming on here... and I know how to get there, but is that as far as I can go / is that the final answer they are looking for?

Also, how do you guys make those fancy equation pictures... theyre so much easier to read!
As mr fantastic said, you have to show that $\displaystyle \displaystyle \lim_{x\to 4} f(x)= f(4)$. So you got "16+ sqrt(3)" for what? The limit? The value of f(4)? If you can show they are both equal to "16+ sqrt(3)" you are done!

To learn how to "make those fancy equation pictures", click on "Learn how to format equations" under mr fantastic's post just above. It will take you to a tutorial forum on LaTex.