limit as x approaches 1 of ((x^{5/2}-2x^{3/2}+x^{1/2}))/(x-1)

解

x \to 1 lim \frac{( x ^{\frac{5}{2}} - 2 x ^{\frac{3}{2}} + x ^{\frac{1}{2}} )}{x - 1}

0

解答ステップ

x \to 1 lim (\frac{x ^{\frac{5}{2}} - 2 x ^{\frac{3}{2}} + x ^{\frac{1}{2}}}{x - 1})

簡素化

\frac{x ^{\frac{5}{2}} - 2 x ^{\frac{3}{2}} + x ^{\frac{1}{2}}}{x - 1} : x^{\frac{1}{2}} (x - 1)

= x \to 1 lim (x^{\frac{1}{2}} (x - 1))

値を挿入する

x = 1

= 1^{\frac{1}{2}} (1 - 1)

簡素化

= 0