limit as h approaches 0 of ((1+h)^6-1)/h

解答

h \to 0 lim (\frac{( 1 + h ) ^{6} - 1}{h})

6

求解步骤

h \to 0 lim (\frac{( 1 + h ) ^{6} - 1}{h})

化简

\frac{( 1 + h ) ^{6} - 1}{h} : (h + 2) ((h + 1)^{4} + (h + 1)^{2} + 1)

= h \to 0 lim ((h + 2) ((h + 1)^{4} + (h + 1)^{2} + 1))

代入值

h = 0

= (0 + 2) ((0 + 1)^{4} + (0 + 1)^{2} + 1)

化简

(0 + 2) ((0 + 1)^{4} + (0 + 1)^{2} + 1) : 6

= 6

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