高数微积分求全导两道计算题,在线等详解?
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1. 分子分母同除以 x^15, 得
lim (1-3/x)^10 (4x+1/x)^5/(1/x-2)^15 = ∞
2. 原式 = limx(2x)/(3x^2) = 2/3
3. 原式 = limln[(1-5/x^2)^(-x^2/5)]^[(5x^2-3)/(x^2/5)]
= limlne^[(5x^2-3)/(x^2/5)] = lim(5x^2-3)/(x^2/5) = 25
4. 原式 = limxln(arccotx) = ∞
5. f' = 1/√(1-x^2), f'' = (-1/2)(1-x^2)^(-3/2)(-2x) = x/(1-x^2)^(3/2)
lim (1-3/x)^10 (4x+1/x)^5/(1/x-2)^15 = ∞
2. 原式 = limx(2x)/(3x^2) = 2/3
3. 原式 = limln[(1-5/x^2)^(-x^2/5)]^[(5x^2-3)/(x^2/5)]
= limlne^[(5x^2-3)/(x^2/5)] = lim(5x^2-3)/(x^2/5) = 25
4. 原式 = limxln(arccotx) = ∞
5. f' = 1/√(1-x^2), f'' = (-1/2)(1-x^2)^(-3/2)(-2x) = x/(1-x^2)^(3/2)
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