Помогите с пределами прошу

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1) [latex] \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}[/latex] 2) [latex] \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[/latex] 3) [latex] \lim_{x \to \infty} \frac{5x^2-12}{x^2+x+1} =\lim_{x \to \infty} \frac{5x^2}{x^2} =5[/latex] 4) [latex] \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}[/latex] 5) [latex] \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}[/latex]