- $\lim_{x\to\infty}(1+\frac1x)^{3x}$
- $lim_{x\to\infty}(1+\frac{1}{x^2})^{3x-4}$
- $lim_{x\to\infty}(\frac{7x+10}{1+7x})^{\frac x3}$
- $\lim_{x\to 0}x^{x}$
- $\lim_{x\to 1}\frac{\sqrt[n]{x}-1}{\sqrt[m]{x}-1}$
- $\lim_{x\to a}\frac{\sqrt{x-b}-\sqrt{a-b}}{x^2-a^2}$
- $\lim_{x\to 1}\frac{x^2-x\sin x}{x-\sin^2x}$
- $\lim_{x\to +\infty}\left(\frac{x+1}{ln x}\right)$
- $\lim_{x\to +\infty}\frac{lnx+2x^2-2x+1}{x}$
- $\lim_{x\to 0^+}ln(\cos x)lnx$
- $\lim_{x\to +\infty}\frac{e^xlnx+1}{x^2}$
- $\lim_{x\to 0}\frac{\sin x+e^x-1}{x^2+x}$
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