Question

Ребята решите хоть что то. Баллами не обижу!!

Answer 1

$displaystyle lim_{x to 0} frac{3x^3+2x}{x^3+x} = lim_{x to 0} frac{x(3x^2+1)}{x(x^2+1)}= lim_{x to 0} frac{3x^2+1}{x^2+1}= frac{3cdot0^2+1}{0^2+1}=1$


$displaystyle lim_{x to 7} frac{x^2-49}{x-7}=lim_{x to 7} frac{(x-7)(x+7)}{x-7}=lim_{x to 7} (x+7)=7+7=14$

$displaystyle lim_{x to 1} frac{x^2-3x+2}{x-1}=lim_{x to 1} frac{x^2-x-2x+2}{x-1}=lim_{x to 1} frac{x(x-1)-2(x-1)}{x-1} =\ \ \=lim_{x to 1} frac{(x-1)(x-2)}{x-1}=lim_{x to 1} (x-2)=1-2=-1$


$displaystyle lim_{x to 0} frac{2x}{sqrt{x+1}-1}=lim_{x to 0} frac{2x(sqrt{x+1}+1)}{x} =2lim_{x to 0} (sqrt{x+1}+1)=4$


$displaystyle lim_{x to 0} frac{sqrt{1+3x^2}-1}{x^2(1+x)}=lim_{x to 0} frac{3x^2}{x^2(1+x)(sqrt{1+3x^2}+1)} =\ \ \ =3lim_{x to 0} frac{1}{(1+x)(sqrt{1+3x^2}+1)} = frac{3}{2}$