lim(3√(x^3+x^2)-4√(x^4+x^3)利用泰勒公式求极限?
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极限过程是什么?
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这是啥呀?最好给图片。
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y=1/x
y->0+
(1+y)^(1/3) = 1+(1/3)y +o(y)
(1+y)^(1/4) = 1+(1/4)y +o(y)
(1+y)^(1/3) -(1+y)^(1/4) =(1/12)y +o(y)
lim(x->+∞) [ (x^3+x^2)^(1/3) -(x^4+x^3)^(1/4) ]
=lim(y->0+) [ (1/y^3+1/y^2)^(1/3) -(1/y^4+1/y^3)^(1/4) ]
=lim(y->0+) [ (1+y)^(1/3) -(1+y)^(1/4) ] /y
=lim(y->0+) (1/12)y/y
=1/12
y->0+
(1+y)^(1/3) = 1+(1/3)y +o(y)
(1+y)^(1/4) = 1+(1/4)y +o(y)
(1+y)^(1/3) -(1+y)^(1/4) =(1/12)y +o(y)
lim(x->+∞) [ (x^3+x^2)^(1/3) -(x^4+x^3)^(1/4) ]
=lim(y->0+) [ (1/y^3+1/y^2)^(1/3) -(1/y^4+1/y^3)^(1/4) ]
=lim(y->0+) [ (1+y)^(1/3) -(1+y)^(1/4) ] /y
=lim(y->0+) (1/12)y/y
=1/12
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