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[Гост]

Lim x->0 [tex]\frac{1+sinx-cosx}{1-sinx-cosx}[/tex]
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[Гост]

[tex]\lim_{x \to 0}\frac{1-\cos x + \sin x}{1-\cos x-\sin x}=\lim_{x \to 0}\frac{2\sin^2 (x/2) + 2\sin (x/2) \cos(x/2)}{2\sin^2 (x/2) - 2\sin (x/2) \cos(x/2)}=[/tex]
[tex]\lim_{x \to 0}\frac{2\sin (x/2)(\sin (x/2) + \cos(x/2))}{2\sin (x/2)(\sin(x/2) - \cos(x/2))}=\lim_{x \to 0}\frac{\sin (x/2) + \cos(x/2)}{\sin(x/2) - \cos(x/2)}=\frac{0+1}{0-1}=-1[/tex]