Question

我是人類

想問這題極限值

(4) lim
x-1
10
X
x¹0 - 1
-1
(x - 1)²
10
x-1
二

Answer 1

✨ 最佳解答 ✨

qn

(x¹⁰-1)/(x-1)²=(x⁹+x⁸+x⁷+x⁶+x⁵+x⁴+x³+x²+x+1)/(x-1)

[(x¹⁰-1)/(x-1)² - 10/(x-1)]
=(x⁹+x⁸+x⁷+x⁶+x⁵+x⁴+x³+x²+x-9)/(x-1)
=x⁸+2x⁷+3x⁶+4x⁵+5x⁴+6x³+7x²+8x+9

當 x→1 , [(x¹⁰-1)/(x-1)² - 10/(x-1)]→1+2+3+4+5+6+7+8+9
=45