大學全冊高等數(shù)學知識點(全)

1、1大學高等數(shù)學知識點整理大學高等數(shù)學知識點整理公式，用法合集公式，用法合集極限與連續(xù)極限與連續(xù)一.數(shù)列函數(shù):1.類型:(1)數(shù)列:()nafn?1()nnafa??(2)初等函數(shù):(3)分段函數(shù):0102()()()xxfxFxxxfx??????00()()xxfxFxxxa??????(4)復合(含)函數(shù):f()()yfuux???(5)隱式(方程):()0Fxy?(6)參式(數(shù)一二):()()xxtyyt?????(7)變限積分函

2、數(shù):()()xaFxfxtdt??(8)級數(shù)和函數(shù)(數(shù)一三):0()nnnSxaxx??????2.特征(幾何):(1)單調(diào)性與有界性(判別)(單調(diào)定號)()fx000()(()())xxxfxfx????(2)奇偶性與周期性(應用).3.反函數(shù)與直接函數(shù):11()()()yfxxfyyfx???????二.極限性質(zhì):1.類型:(含)(含)limnna??lim()xfx??x???0lim()xxfx?0xx??2.無窮小與無窮大(注

3、:無窮量):3.未定型:0001000?????????4.性質(zhì):有界性保號性歸并性三.常用結(jié)論:11nn?1(0)1naa??1()max()nnnnabcabc?????00!naan??3(2)冪指型處理:(如:)()()ln()()vxvxuxuxe?1111111(1)xxxxxeeee??????(3)含變限積分(4)不能用與不便用7.泰勒公式(皮亞諾余項):處理和式中的無窮小8.極限函數(shù):(分段函數(shù))()lim()nfxF

4、xn????六.非常手段1.收斂準則:(1)()lim()nxafnfx?????(2)雙邊夾:nnnbac??nnbca?(3)單邊擠:1()nnafa??21aa?naM?()0fx?2.導數(shù)定義(洛必達):00lim()xffxx??:::3.積分和:10112lim[()()()]()nnffffxdxnnnn????????4.中值定理:lim[()()]lim()xxfxafxaf??????????5.級數(shù)和(數(shù)一三):(

5、1)收斂(如)(2)1nna???lim0nna????2!limnnnnn??121lim()nnnnaaaa??????????(3)與同斂散na11()nnnaa?????七.常見應用:1.無窮小比較(等價階):()(0)nfxkxx?:(1)(1)()(0)(0)(0)0(0)nnffffa????????()()!!nnnaafxxxxnn???:(2)00()xxnftdtktdt??:2.漸近線(含斜):(1)()liml