数学分析求极限题目 裴礼文 1.3.15 非常感谢
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(1+x)^a ~ 1 + a*x
(x^6+x^5)^(1/6) = x*(1+1/x)^(1/6)
x*(1+1/x)^(1/6) ~ x*( 1 + (1/6)*(1/x) )
x*(1 + (1/6)*(1/x)) = x + x/(6*x) = x + 1/6
(x^6+x^5)^(1/6) ~ x + 1/6
(x^6-x^5)^(1/6) ~ x - 1/6
lim (x^6+x^5)^(1/6) - (x^6-x^5)^(1/6)
= lim (x + 1/6) - (x - 1/6)
= 1/3
(x^6+x^5)^(1/6) = x*(1+1/x)^(1/6)
x*(1+1/x)^(1/6) ~ x*( 1 + (1/6)*(1/x) )
x*(1 + (1/6)*(1/x)) = x + x/(6*x) = x + 1/6
(x^6+x^5)^(1/6) ~ x + 1/6
(x^6-x^5)^(1/6) ~ x - 1/6
lim (x^6+x^5)^(1/6) - (x^6-x^5)^(1/6)
= lim (x + 1/6) - (x - 1/6)
= 1/3
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