Граница х клони към 0

[Sweetbubble]

[tex]\lim_{x \to 0}x[/tex] [tex]\frac{xsinx}{1-cosx}[/tex]

[Nathi123]

[tex]\lim_{x \to 0}\frac{xsinx}{1-cosx}=\lim_{x \to 0}\frac{2xsin\frac{x}{2}cos\frac{x}{2}}{2sin^{2}\frac{x}{2}}=2\lim_{x \to 0}\frac{\frac{x}{2}}{sin\frac{x}{2}}=2.1=2[/tex] Използва се,че [tex]\lim_{x \to 0}cos\frac{x}{2}=cos0=1[/tex].