1.\:\:\lim _{x\to 0}((1+2x)^{\frac{3}{x}})
2.\:\:\lim _{x\to \infty}(6+\frac{\sin (x)}{\sqrt{x}})
3.\:\:\lim _{x\to 0}(\frac{\sin(3x)}{x})
4.\:\:\lim _{x\to \infty}(x-\ln (x))
5.\:\:\lim _{x\to \infty}(\frac{5^x}{3^x+2^x})
6.\:\:\lim _{x\to \infty}(\frac{e^{3x}-e^{-3x}}{e^{3x}+e^{-3x}})
7.\:\:\lim _{x\to 0+}(\frac{1}{1+2^{-\frac{1}{x}}})
8.\:\:\lim _{x\to \infty}(x^{2}3^{-x})
9.\:\:\lim _{x\to 0}(\frac{\sin (2x)}{3x})
10.\:\:\lim _{x\to 0}(\frac{x^{2}\sin(\frac{1}{x})}{\sin(x)})
