Question

how do i solve for this limit algebraically? lim x goes to 4 of square root of(5-x) -1 / 2 - square root of(x)? i multiplied by both conjugates and got 0 for the top and 2 for the botton is that right?

Answer 1

\[\lim_{x\to 4}\frac{\sqrt{5-x}-1}{2-\sqrt{x}}\]?

Answer 2

yes when i solved for it algebraically, i got 0 for the top and 2 for the bottom is that correct>?

Answer 3

no, you should get 0/0

Answer 4

then multiply by conjugates
\[\frac{\sqrt{5-x}-1}{2-\sqrt{x}}*\frac{(\sqrt{5-x}+1)(2+\sqrt{x})}{(\sqrt{5-x}+1)(2+\sqrt{x})} = \frac{(4-x)(2+\sqrt{x})}{(4-x)(\sqrt{5-x}+1)} = \frac{2+\sqrt{x}}{\sqrt{5-x}+1}\]

evaluate at x=4
limit = 2