limit as h approaches 0 of ((1+h)^8-1)/h

解答

h \to 0 lim (\frac{( 1 + h ) ^{8} - 1}{h})

8

求解步骤

h \to 0 lim (\frac{( 1 + h ) ^{8} - 1}{h})

化简

\frac{( 1 + h ) ^{8} - 1}{h} : (h^{2} + 2 h + 2 h + 2 + 2) (h^{2} + 2 h - 2 h + 2 - 2) (h^{2} + 2 h + 2) (h + 2)

= h \to 0 lim ((h^{2} + 2 h + 2 h + 2 + 2) (h^{2} + 2 h - 2 h + 2 - 2) (h^{2} + 2 h + 2) (h + 2))

代入值

h = 0

= (0^{2} + 2 \cdot 0 + 2 \cdot 0 + 2 + 2) (0^{2} + 2 \cdot 0 - 2 \cdot 0 + 2 - 2) (0^{2} + 2 \cdot 0 + 2) (0 + 2)

化简

(0^{2} + 2 \cdot 0 + 2 \cdot 0 + 2 + 2) (0^{2} + 2 \cdot 0 - 2 \cdot 0 + 2 - 2) (0^{2} + 2 \cdot 0 + 2) (0 + 2) : 8

= 8

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