Намерете

[Гост]

[tex]\lim_{x \to 0} \frac{5x-sinx}{3x+sinx}[/tex]

[S.B.]

[tex]\lim_{x \to 0} \frac{5x-sinx}{3x+sinx}[/tex]

[tex]\lim_{x \to 0} \displaystyle\frac{5x - \sin x}{3x + \sin x}= \displaystyle\lim_{x \to 0} \frac{x(5 - \displaystyle\frac{\sin x}{x}) }{x(3 + \displaystyle \frac{\sin x}{x} )} = \lim_{x \to 0}\displaystyle \frac{5 - 1}{3 + 1} = \displaystyle\frac{4}{4} = 1[/tex]