Question

Решить пределы

$\lim_{ \to \-3}$$\frac{\sqrt{x+10}-\sqrt{4-x} }{2x^{2} -x-21}$

$\lim_{ \to \ 0} \frac{cosx-cos5x}{2x^{2} }$

Answer 1

$1)\; \; \lim\limits _{x \to 3}\frac{\sqrt{x+10}-\sqrt{4-x}}{2x^2-x-21}=\frac{\sqrt{13}-\sqrt{1}}{18-3-21}=-\frac{\sqrt{13}-1}{6}=\frac{1-\sqrt{13}}{6}\\\\\\2)\; \; \lim\limits _{x \to 0}\frac{cosx-cos5x}{2x^2}=\lim\limits _{x \to 0}\frac{2sin3x\cdot sin2x}{2x^2}=\Big [\; sin\alpha \sim \alpha \; ,\; \alpha \to o\; \Big ]=\\\\=\lim\limits _{x \to 0}\frac{2\cdot 3x\cdot 2x}{2x^2}=\lim\limits _{x \to 0}\frac{12x^2}{2x^2} =6$