limit as x approaches 1 of (x^{10}-1)/(x-1)

解

x \to 1 lim (\frac{x ^{10} - 1}{x - 1})

10

解答ステップ

x \to 1 lim (\frac{x ^{10} - 1}{x - 1})

簡素化

\frac{x ^{10} - 1}{x - 1} : (x + 1) (x^{4} - x^{3} + x^{2} - x + 1) (x^{4} + x^{3} + x^{2} + x + 1)

= x \to 1 lim ((x + 1) (x^{4} - x^{3} + x^{2} - x + 1) (x^{4} + x^{3} + x^{2} + x + 1))

値を挿入する

x = 1

= (1 + 1) (1^{4} - 1^{3} + 1^{2} - 1 + 1) (1^{4} + 1^{3} + 1^{2} + 1 + 1)

簡素化

(1 + 1) (1^{4} - 1^{3} + 1^{2} - 1 + 1) (1^{4} + 1^{3} + 1^{2} + 1 + 1) : 10

= 10