一道高等函数题目(关于L'Hospital法则和极限)已知f(a)的有二阶导数,求lim(h趋向于0)(f(a+h)+f(a-h)-2f(a))/h^2答案是f''(a),用L'Hospital法则易证出,但lim(f(a+h)-f(a))/h=lim(f(a)-f(a-h))/h=f'(a)代入之,得到0
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![一道高等函数题目(关于L'Hospital法则和极限)已知f(a)的有二阶导数,求lim(h趋向于0)(f(a+h)+f(a-h)-2f(a))/h^2答案是f''(a),用L'Hospital法则易证出,但lim(f(a+h)-f(a))/h=lim(f(a)-f(a-h))/h=f'(a)代入之,得到0](/uploads/image/z/7544743-7-3.jpg?t=%E4%B8%80%E9%81%93%E9%AB%98%E7%AD%89%E5%87%BD%E6%95%B0%E9%A2%98%E7%9B%AE%EF%BC%88%E5%85%B3%E4%BA%8EL%27Hospital%E6%B3%95%E5%88%99%E5%92%8C%E6%9E%81%E9%99%90%EF%BC%89%E5%B7%B2%E7%9F%A5f%EF%BC%88a%EF%BC%89%E7%9A%84%E6%9C%89%E4%BA%8C%E9%98%B6%E5%AF%BC%E6%95%B0%2C%E6%B1%82lim%28h%E8%B6%8B%E5%90%91%E4%BA%8E0%29%EF%BC%88f%28a%2Bh%29%2Bf%28a-h%29-2f%28a%29%EF%BC%89%2Fh%5E2%E7%AD%94%E6%A1%88%E6%98%AFf%27%27%28a%29%2C%E7%94%A8L%27Hospital%E6%B3%95%E5%88%99%E6%98%93%E8%AF%81%E5%87%BA%2C%E4%BD%86lim%28f%28a%2Bh%29-f%28a%29%29%2Fh%3Dlim%28f%28a%29-f%28a-h%29%29%2Fh%3Df%27%28a%29%E4%BB%A3%E5%85%A5%E4%B9%8B%2C%E5%BE%97%E5%88%B00)
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