1. [TEX]\lim_{x\to0}{\frac{(x^2+2010)\sqrt[7]{1-2x} - 2010}{x}[/TEX]
[TEX]= \lim_{x\to0}{\frac{(x^2+2010)(\sqrt[7]{1-2x}-1)+x^2}{x}[/TEX]
[TEX]= \lim_{x\to0}{\frac{(x^2+2010)(\sqrt[7]{1-2x}-1)}{x} +\lim_{x\to0}{x}[/TEX]
[TEX] = \lim_{x\to0}{\frac{(x^2+2010).(-2x)}{x.(\sqrt[7]{(1-2x)^6} +\sqrt[7]{(1-2x)^5} + \sqrt[7]{(1-2x)^4} + \sqrt[7]{(1-2x)^3} + \sqrt[7]{(1-2x)^2} + \sqrt[7]{1-2x}+1)}}[/TEX]
[TEX] = \lim_{x\to0}{\frac{(x^2+2010).(-2)}{\sqrt[7]{(1-2x)^6}+\sqrt[7]{(1-2x)^5}+\sqrt[7]{(1-2x)^4}+\sqrt[7]{(1-2x)^3}+\sqrt[7]{(1-2x)^2}+\sqrt[7]{1-2x}+1}[/TEX]
[TEX] = \frac{-4020}{7}[/TEX]
2. [TEX] \lim_{x\to0}{\frac{\sqrt{1+2x} -\sqrt[3]{1+3x}}{x^2}[/TEX]
[TEX]= \lim_{x\to0}{\frac{\sqrt{1+2x} -1}{x^2} - \lim_{x\to0}{\frac{\sqrt[3]{1+3x} - 1}{x^2}[/TEX]
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