已知x→0时,(1+ax^2)^(1/3)-1与cosx-1是等价无穷小,则常数a=?

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已知x→0时,(1+ax^2)^(1/3)-1与cosx-1是等价无穷小,则常数a=?

已知x→0时,(1+ax^2)^(1/3)-1与cosx-1是等价无穷小,则常数a=?
已知x→0时,(1+ax^2)^(1/3)-1与cosx-1是等价无穷小,则常数a=?

已知x→0时,(1+ax^2)^(1/3)-1与cosx-1是等价无穷小,则常数a=?
x→0时,(1+ax^2)^(1/3)-1≈1+ax²/3-1=ax²/3
cosx-1≈1-½sin²x-1=½sin²x≈x²/2
ax²/3=x²/2
a=3/2