Question

Помогите с пределами прошу

Answer 1

1) $lim_{x to 3} frac{5x^2-16x+3}{x^2-9} = lim_{x to 3} frac{5(x-0,2)(x-3)}{(x+3)(x-3)}=lim_{x to 3} frac{5x-1}{(x+3)}= frac{14}{6}=frac{7}{3}$



2) $lim_{x to 7} frac{x-7}{ sqrt{11-x}-2}= lim_{x to 7} frac{(x-7)(sqrt{11-x}+2)}{( sqrt{11-x}-2)(sqrt{11-x}+2)}=\ =lim_{x to 7} frac{(x-7)(sqrt{11-x}+2)}{(11-x- 4)}=lim_{x to 7} frac{(x-7)(sqrt{11-x}+2)}{(7-x)}=\ -lim_{x to 7} frac{(x-7)(sqrt{11-x}+2)}{(x-7)}= -lim_{x to7} sqrt{11-x}+2=-4$


3) $lim_{x to infty} frac{5x^2-12}{x^2+x+1} =lim_{x to infty} frac{5x^2}{x^2} =5$



4) $lim_{x to 0} frac{sin3x*sin5x}{2x^2} =lim_{x to 0} frac{3x*5x}{2x^2}=lim_{x to 0} frac{15x^2}{2x^2}=frac{15}{2}$



5) $lim_{x to 0} (1+5x)^{frac{3}{x}}= lim_{x to 0} (1+5x)^{frac{3}{x}*frac{5}{3}}=lim_{x to 0} e^{15}=e^{15}$

Answer 2

что со счетом