一道高数微分题目,用泰勒公式做Lim(n->0)(x^2/2+1-(1+x^2)^(1/2))/(x^2*(sinx)^2)用泰勒公式求解
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![一道高数微分题目,用泰勒公式做Lim(n->0)(x^2/2+1-(1+x^2)^(1/2))/(x^2*(sinx)^2)用泰勒公式求解](/uploads/image/z/7248797-53-7.jpg?t=%E4%B8%80%E9%81%93%E9%AB%98%E6%95%B0%E5%BE%AE%E5%88%86%E9%A2%98%E7%9B%AE%2C%E7%94%A8%E6%B3%B0%E5%8B%92%E5%85%AC%E5%BC%8F%E5%81%9ALim%28n-%3E0%29%28x%5E2%2F2%2B1-%281%2Bx%5E2%29%5E%281%2F2%29%29%2F%28x%5E2%2A%28sinx%29%5E2%29%E7%94%A8%E6%B3%B0%E5%8B%92%E5%85%AC%E5%BC%8F%E6%B1%82%E8%A7%A3)
一道高数微分题目,用泰勒公式做Lim(n->0)(x^2/2+1-(1+x^2)^(1/2))/(x^2*(sinx)^2)用泰勒公式求解
一道高数微分题目,用泰勒公式做
Lim(n->0)(x^2/2+1-(1+x^2)^(1/2))/(x^2*(sinx)^2)用泰勒公式求解
一道高数微分题目,用泰勒公式做Lim(n->0)(x^2/2+1-(1+x^2)^(1/2))/(x^2*(sinx)^2)用泰勒公式求解
由泰勒公式有(1+x^2)^(1/2)=1+x^2/2-x^4/8+O(x^4)
sinx=x+0(x^2) ,则原式=【x^4/8-O(x^4)】/ x^2*(x^2+0(x^3))=【x^4/8-O(x^4)】/ x^4+0(x^4))=1/8