limit as x approaches infinity of (x,x,(sqrt(x)+x^2))/((2x-x^2))

解

x \to \infty lim (\frac{x , x , ( x + x ^{2} )}{( 2 x - x ^{2} )})

(,,) \frac{\infty}{- \infty}

解答ステップ

x \to \infty lim (\frac{x , x , ( x + x ^{2} )}{2 x - x ^{2}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= (,,) \cdot x \to \infty lim (\frac{xx ( x + x ^{2} )}{2 x - x ^{2}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= (,,) \frac{lim _{x \to \infty} ( xx ( x + x ^{2} ) )}{lim _{x \to \infty} ( 2 x - x ^{2} )}

x \to \infty lim (xx (x + x^{2})) = \infty

x \to \infty lim (2 x - x^{2}) = - \infty

= (,,) \frac{\infty}{- \infty}