Evaluate lim(x→0)⁡〖(∛(ax+1)-1)/x〗where a is a constant?

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2007-12-08 14:42:19 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

Using l'Hôpital's rule,
lim(x→0)⁡〖(∛(ax+1)-1)/x〗
= lim(x→0)⁡〖d(∛(ax+1)-1)/dx〗
= lim(x→0)⁡〖a*(ax+1)^(-2/3)〗
= a

2007-12-08 15:19:25 · answer #1 · answered by Hahaha 7 · 0⤊ 0⤋

Hahaha is right, che ( =she or he) just forgot that
d(ax+1)^1/3 = 1/3a(ax+1)^(-2/3), which when x goes to zero becomes 1/3a.

2007-12-08 23:43:44 · answer #2 · answered by Master Math 1 · 0⤊ 0⤋