高等數(shù)學(xué)上復(fù)習(xí)要點

高等數(shù)學(xué)（1）期末復(fù)習(xí)提相

第一章函數(shù)f(x)中符號f xf(xf(xf(xyxf(x)f(x)f(x稱為奇函數(shù)，奇函數(shù)的圖形關(guān)于原點對稱。yyxya

(為實數(shù)(a0,a④對數(shù)函數(shù)：yloga (a0,asinxcosxtanxcotyearctan2(1yeuuv2varctanww1x。分解后的函數(shù)前三個都是基本第二 極限與連(a2xk(a2xka)(a2xka2xk xk(a2xk x2ax (xx)(xx 1x x x x axnaxn1 x

n

n

n0xx0bxmb10

bm1x

nlimsinx lim(11)

e （或lim(1xx

elimsin(x)(x)011lim(1 f(x) （或lim1g(x

ef( f

g(xsin limsinlimsinxlim1 1 1x0sin x03sin 3limsin 2 2 ) )2 )lim(x2)

lim

lim

xx x11 x(11) lim[(11)x x xx0f(xxx0xx0f(x第三 導(dǎo)數(shù)與微f(xxx0

f(x0x)f(x0x

f(x)f(x0xf(xxx0f(x0y

f(x上點(x0,f(x0yf(x在點(x0,f(x0yf(x0)(xx0)f(x0在x0點不一x3xx3xlny1ln(x1)1ln(x

y

yy

2(xxx3x

3(xx6(x2xxy dy(t) d(uv)dud(uv)vdu

v

)vdu

(vdyyxdxyuuxdx第四章導(dǎo)數(shù)的應(yīng)用 若在區(qū)間(a,bf(x)0f(x在區(qū)間(a,b上單調(diào)增加；若在區(qū)間(abf(x)0f(x在區(qū)間(abf(xxx0f(x00f(xxx0的左右由正變負(fù)（f(x00），xx0f(xf(xxx0的左右由負(fù)變正（f(x00），xx0f(x若在區(qū)間(a,bf(x)0f(x在區(qū)間(a,b上是凹函數(shù)；若在區(qū)間(a,bf(x)0f(x在區(qū)間(ab

f(xa

f(x)ayayf(x

f(xxx0yf(xf(x在區(qū)間[abf(xf(x第五 不定積(f(x)g(x))dxf(x)dxcf(x)dxcf (c[k1f1(x)k2f2(x)]dxk1f1(x)dxk2f2d f(x)dx

fF(x)dxF(x)及df(x)dxfdF(x)F(x)在利用分部積分時，如何選擇uv將排在后面的函數(shù)選做v，具體地說：若被積函數(shù)是x3e2x，則將e2x選做v；若被積函數(shù)是x2arctanx，則將x2選做v。 a(k1f1(x)k2f2(x))dxk1af1(x)dxk2af2 af(x)dxaf(x)dxcf

af(x)dxbfaaf(x)dxa若G(x) f(t)dt，G(x)f p1p1 10xpp1p1yf(xyg(xxa,xbSbSaf(x)g(x)對于對稱區(qū)間(a,a)a當(dāng)f(x)為奇函數(shù)時 f(x)dx 當(dāng)f(x)為偶函數(shù)時 －af(x)dx20f(x)dx2－af第七 無窮級 若an和bn收斂，則(anbn (anbn)an

若anc為常數(shù)，則can can 級數(shù)收斂的必要條件：若an收斂，則liman0 幾何級數(shù)aqnq1q1 npn

p1p1⒌知道函數(shù)的泰勒級數(shù)和馬克勞林級數(shù)，記住ex,sinx,cosx和ln(1x anbn(n1,2,，那么

第八 常微分方y(tǒng)p(xyq(x