Question

найдите...................

Answer 1

$lim_{x to 2} frac{ x^{2} +6}{ x^{2} +1} = frac{ 2^{2} +6}{ 2^{2} +1} = frac{10}{5} =2$
$lim_{x to 2} frac{ x^{2} -4}{x-2} = frac{ 2^{2} -4}{x-2} = frac{0}{0}$
неопределенность вида 0/0
$lim_{x to 2} frac{ x^{2} -4}{x-2} = lim_{x to 2} frac{(x+2)*(x-2)}{x-2} = lim_{x to 2} (x+2)=2+2=4$
$lim_{x to 0} frac{sin12x}{6x}$
$lim_{x to 0} frac{sin alpha }{ alpha } =1$ - первый замечательный предел
$lim_{x to 0} frac{sin12x}{6x} = lim_{x to 0} frac{2*sin12x}{2*6x} =2* lim_{x to 0} frac{sin12x}{12x}=2*1=2$