Question

Lim (х стремится к бесконечности) x^2-x+1/5x+x^2

Answer 1

$lim_{x to infty} dfrac{x^2 - x + 1}{5x + x^2} = lim_{x to infty} dfrac{ dfrac{x^2}{x^2} - dfrac{x}{x^2} + dfrac{1}{x^2} }{ dfrac{5x}{x^2} + dfrac{x^2}{x^2} } = lim_{x to infty} dfrac{1 - dfrac{1}{x}+dfrac{1}{x^2}}{dfrac{5}{x}+1} =\ \ = dfrac{1}{1} = 1$