H hank Junior Member Joined Sep 13, 2006 Messages 209 Sep 21, 2006 #1 Here's the problem... Find the limit as x->1 of (1 - x^(1/2)) / (1 - x) I attempted it by trying to multiply by the conjugate, but that doesn't work. Can anyone give me a hint?
Here's the problem... Find the limit as x->1 of (1 - x^(1/2)) / (1 - x) I attempted it by trying to multiply by the conjugate, but that doesn't work. Can anyone give me a hint?
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Sep 21, 2006 #2 Yes, it'll work. Multiply top and bottom by the conjugate of the numerator: \(\displaystyle \L\\\frac{1-\sqrt{x}}{1-x}\cdot\frac{1+\sqrt{x}}{1+\sqrt{x}}\\=\frac{1-x}{(1-x)(1+\sqrt{x})}\) Now, cancel what will cancel. See the limit?.
Yes, it'll work. Multiply top and bottom by the conjugate of the numerator: \(\displaystyle \L\\\frac{1-\sqrt{x}}{1-x}\cdot\frac{1+\sqrt{x}}{1+\sqrt{x}}\\=\frac{1-x}{(1-x)(1+\sqrt{x})}\) Now, cancel what will cancel. See the limit?.
