# Evaluate the limit

• Jan 29th 2010, 11:58 AM
mj226
Evaluate the limit
Evaluate the limit of 4-x/2-√x as x approaches 4

I believe that this function is in indeterminate form. I just cant seem to rewrite the function so that i can find the limit ( if it exists).

If anyone can explain how to evaluate this limit, I would be very grateful.
• Jan 29th 2010, 12:03 PM
Bruno J.
You should use parentheses to write this expression. It could mean at least 4 different things, but as stated it means $4-\frac x 2 - \sqrt x$.
• Jan 29th 2010, 12:04 PM
Quote:

Originally Posted by mj226
Evaluate the limit of 4-x/2-√x as x approaches 4

I believe that this function is in indeterminate form. I just cant seem to rewrite the function so that i can find the limit ( if it exists).

If anyone can explain how to evaluate this limit, I would be very grateful.

Multiply by $\frac{2+\sqrt{x}}{2+\sqrt{x}}$

$\lim_{x->4}\frac{4-x}{2-\sqrt{x}}\left(\frac{2+\sqrt{x}}{2+\sqrt{x}}\right )=\lim_{x->4}\frac{(4-x)(2+\sqrt{x})}{4-x}$

$=\lim_{x->4}(2+\sqrt{x})$

$=4$
• Jan 29th 2010, 12:09 PM
mj226
Sorry about the parentheses. It should have been (4-x)/(2-x^1/2)

Oh. I see. Thank You.
• Jan 29th 2010, 12:16 PM
General
Quote:

Originally Posted by mj226
Sorry about the parentheses. It should have been (4-x)/(2-x^1/2)

Oh. I see. Thank You.

There is another one.
$4-x=(2)^2-(\sqrt{x})^2=(2-\sqrt{x})(2+\sqrt{x})$
Bad guys cancel, and you are done.