Oblicz granice funkcji a) [latex] lim_{x o -1} frac{ x^{2} -1}{x^{2}+3x+2} [/latex] b) [latex] lim_{x o 0} frac{ x^{4} + x^{3}}{ x^{4} - 2x^{3}} [/latex] c) [latex] lim_{x o 0} frac{ sqrt{1+x} - sqrt{1-x}}{x}[/latex]

a) [latex]lim limits_{x o -1} frac{x^2-1}{x^2+3x+2}= lim limits_{x o -1} frac{(x-1)(x+1)}{x^2+2x+x+2}= lim limits_{x o -1} frac{(x-1)(x+1)}{x(x+2)+x+2}= \ \ lim limits_{x o -1} frac{(x-1)(x+1)}{(x+1)(x+2)}= lim limits_{x o -1} frac{x-1}{x+2}= frac{-2}{1}=-2[/latex] b) [latex]lim limits_{x o 0} frac{x^4+x^3}{x^4-2x^3}= lim limits_{x o 0} frac{x^3(x+1)}{x^3(x-2)}= lim limits_{x o 0} frac{x+1}{x-2}= frac{1}{-2} = -frac{1}{2}[/latex] c) [latex]lim limits_{x o 0} frac{sqrt{1+x} - sqrt{1-x}}{x} = lim limits_{x o 0} frac{1+x-(1-x)}{x(sqrt{1+x}+sqrt{1-x})}= lim limits_{x o 0} frac{2x}{x(sqrt{1+x}+sqrt{1-x})}= \ \ lim limits_{x o 0} frac{2}{sqrt{1+x}+sqrt{1-x}}= frac{2}{2}=1[/latex] hmm