Solve lim - - x rightarrow 0 - dfrac - sqrt - 2 - x - - sqrt - 2 - - - x -

Question

Toppr Admin · Accepted Answer

Limx-x2192-0-x221A-2-x-x2212-x221A-2x-xD7-x221A-2-x-x221A-2-x221A-2-x-x221A-2-limx-x2192-0-2-x-x2212-2x-x221A-2-x-x221A-2-limx-x2192-0-1-x221A-2-x-x221A-2-12-x221A-2-

Solve ${lim}_{x \to 0} \frac{\sqrt{2 + x} - \sqrt{2}}{x}$

${lim}_{x \to 0} (\frac{\sqrt{2 + x} - \sqrt{2}}{x}) \times (\frac{\sqrt{2 + x} + \sqrt{2}}{\sqrt{2 + x} + \sqrt{2}}) = {lim}_{x \to 0} (\frac{(2 + x) - 2}{x (\sqrt{2 + x} + \sqrt{2})}) = {lim}_{x \to 0} (\frac{1}{(\sqrt{2 + x} + \sqrt{2})}) = (\frac{1}{2 \sqrt{2}})$

Solve limx→0√2+x−√2x

limx→0(√2+x−√2x)×(√2+x+√2√2+x+√2)=limx→0((2+x)−2x(√2+x+√2))=limx→0(1(√2+x+√2))=(12√2)

Solve ${lim}_{x \to 0} \frac{\sqrt{2 + x} - \sqrt{2}}{x}$

${lim}_{x \to 0} (\frac{\sqrt{2 + x} - \sqrt{2}}{x}) \times (\frac{\sqrt{2 + x} + \sqrt{2}}{\sqrt{2 + x} + \sqrt{2}}) = {lim}_{x \to 0} (\frac{(2 + x) - 2}{x (\sqrt{2 + x} + \sqrt{2})}) = {lim}_{x \to 0} (\frac{1}{(\sqrt{2 + x} + \sqrt{2})}) = (\frac{1}{2 \sqrt{2}})$