<s>[INST] What are good ways to find the limits of this function? Compute: $\displaystyle\lim_{x\rightarrow 2}\frac{\sqrt{x+1}-\sqrt{ 1-x}}{x}$
 [/INST] I assume you are interested in $$\lim_{x \to 0} \dfrac{\sqrt{1+x} - \sqrt{1-x}}x$$
Multiply and divide by $\sqrt{1+x} + \sqrt{1-x}$ to get
$$\dfrac{\sqrt{1+x} - \sqrt{1-x}}x \times \dfrac{\sqrt{1+x} + \sqrt{1-x}}{\sqrt{1+x} + \sqrt{1-x}} = \dfrac{(1+x)-(1-x)}{x(\sqrt{1+x} + \sqrt{1-x})} = \dfrac{2x}{x(\sqrt{1+x} + \sqrt{1-x})}\\ = \dfrac2{\sqrt{1+x} + \sqrt{1-x}}$$
Now can you finish it off?
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