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Why don't multiply numerator and denominator by $\displaystyle \sqrt{x} + \sqrt{a}$?...\(\displaystyle \lim_{x \to a} \frac{ x^2 - a^2}{\sqrt(x) - \sqrt(a)}\)
I've tried to solve this standard, but I either end up with 0 in the denominator, or I end up with 0/0.
Any hints on what to do with this next?
Thanks
I tried that, however I end up with x - a, at the bottom, which leads to 0 in the denominator.Why don't multiply numerator and denominator by $\displaystyle \sqrt{x} + \sqrt{a}$?...
Kind regards
$\chi$ $\sigma$
$\displaystyle \frac{x^{2} - a^{2}}{\sqrt{x}-\sqrt{a}}\ \frac{\sqrt{x} + \sqrt{a}}{\sqrt{x} + \sqrt{a}} = \frac{x^{2}-a^{2}}{x-a}\ (\sqrt{x}+\sqrt{a})= (x+a)\ (\sqrt{x}+\sqrt{a})$I tried that, however I end up with x - a, at the bottom, which leads to 0 in the denominator.
\(\displaystyle \frac{x^2\sqrt(x) + x^2 \sqrt(a) - a^2\sqrt(x) - a^2\sqrt(a)}{x-a}\)
Ohh ok, I should have seen that.$\displaystyle \frac{x^{2} - a^{2}}{\sqrt{x}-\sqrt{a}}\ \frac{\sqrt{x} + \sqrt{a}}{\sqrt{x} + \sqrt{a}} = \frac{x^{2}-a^{2}}{x-a}\ (\sqrt{x}+\sqrt{a})= (x+a)\ (\sqrt{x}+\sqrt{a})$
Kind regards
$\chi$ $\sigma$
It should technically be \[\color{red}{\lim\limits_{x\to a}} x\sqrt{x}+x\sqrt{a}+a\sqrt{x}+a\sqrt{a} = 4a\sqrt{a}\]Ohh ok, I should have seen that.
\(\displaystyle x\sqrt(x) + x\sqrt(a) + a\sqrt(x) + a\sqrt(a)\)
\(\displaystyle = 4a\sqrt(a)\)
That seem right?
Just a $\LaTeX$ tip:\(\displaystyle \lim_{x \to a} \frac{ x^2 - a^2}{\sqrt(x) - \sqrt(a)}\)
I've tried to solve this standard, but I either end up with 0 in the denominator, or I end up with 0/0.
Any hints on what to do with this next?
Thanks