limit as x approaches 0 of ((1+x)^4-1)/x

解答

x \to 0 lim (\frac{( 1 + x ) ^{4} - 1}{x})

4

求解步骤

x \to 0 lim (\frac{( 1 + x ) ^{4} - 1}{x})

化简

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

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

代入值

x = 0

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

化简

(0^{2} + 2 \cdot 0 + 2) (0 + 2) : 4

= 4

in v erse l a pl a ce \frac{- 3 s + 9}{( s + 3 ) ^{2}}

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