Question

Need help !!! The steps please for those who solve this problem. Thank you

Answer 1

[tex] \lim\limits_{x\to3b}\dfrac{\sqrt{x}-\sqrt{3b}-\sqrt{x-3b}}{\sqrt{x^2-9b^2}} =\lim\limits_{x\to3b}\dfrac{\sqrt{x}-\sqrt{3b}}{\sqrt{x^2-9b^2}} -\lim\limits_{x\to3b}\,\dfrac{\sqrt{x-3b}}{\sqrt{x^2-9b^2}} =\lim\limits_{x\to3b}\,\dfrac{x-3b}{(\sqrt{x}+\sqrt{3b})\sqrt{(x+3b)(x-3b)}} -\lim\limits_{x\to3b}\,\dfrac{\sqrt{x-3b}}{\sqrt{(x+3b)(x-3b)}} = \lim\limits_{x\to3b}\,\dfrac{\sqrt{x-3b}}{(\sqrt{x}+\sqrt{3b})\sqrt{x+3b}} -\lim\limits_{x\to3b}\,\dfrac{1}{\sqrt{x+3b}} [/tex]

[tex]=\dfrac{\sqrt{3b-3b}}{(\sqrt{3b}+\sqrt{3b})\sqrt{3b+3b}} -\dfrac{1}{\sqrt{3b+3b}} = 0 - \dfrac{1}{\sqrt{6b}} =-\dfrac{1}{\sqrt{6b}}[/tex]