Задача 73778 ...

650a00499685cd7da7a8fd2d

28.10.2023 15:26:59

lim_(x→0) (sin7x-sin2x)/sinx

5f3ea7e3faf909182968ddd9

28.10.2023 20:16:23

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[m]lim_{x → 0}\frac{sin7x-sin2x}{sinx}=\frac{0}{0}=lim_{x → 0}\frac{2sin\frac{7x-2x}{2}\cdot cos\frac{7x+2x}{2}}{sinx}=[/m]

[m]lim_{x → 0}\frac{2sin\frac{5x}{2}\cdot cos\frac{9x}{2}}{sinx}=2\cdot lim_{x →0}cos\frac{9x}{2}\cdot lim_{x →0}\frac{sin\frac{5x}{2}}{sinx}=2\cdot cos0\cdot lim_{x → 0}\frac{sin\frac{5x}{2}}{\frac{2}{5}\cdot \frac{5x}{2}}\cdot \frac{x}{sinx}=2\cdot 1\cdot \frac{1}{\frac{2}{5}}\cdot 1\cdot 1=5[/m]