A) \[0\]
B) \[7\sqrt{2}\]
C) \[4\sqrt{7}\]
D) \[2\sqrt{7}\]
Correct Answer: D
Solution :
\[\underset{x\to 3}{\mathop{\lim }}\,\,\frac{3-x}{\sqrt{4+x}-\sqrt{1+2x}}\] \[=\underset{x\to 3}{\mathop{\lim }}\,\,\frac{(3-x)\,(\sqrt{4+x}+\sqrt{1+2x)}}{{{(\sqrt{4+x})}^{2}}-{{(\sqrt{1+2x})}^{2}}}\] \[=\underset{x\to 3}{\mathop{\lim }}\,\frac{(3-x)\,(\sqrt{4+x}+\sqrt{1+2x})}{4+x-1-2x}\] \[=\underset{x\to 3}{\mathop{\lim }}\,\frac{(3-x)\,(\sqrt{4+x}+\sqrt{1+2x})}{3-x}\] \[=\underset{x\to 3}{\mathop{\lim }}\,\,\sqrt{4+x}+\sqrt{1+2x}\] \[=\sqrt{4+3}+\sqrt{1+6}\] \[=\sqrt{7}+\sqrt{7}=2\sqrt{7}\]
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