2019電大高等數(shù)學(xué)小抄

1、復(fù)習(xí)資料高等數(shù)學(xué)基礎(chǔ)模擬練習(xí)題一、單項(xiàng)選擇題1.設(shè)函數(shù)的定義域?yàn)椋瑒t函數(shù)的圖形關(guān)于（C）對稱)(xf)(????)()(xfxf??(A)(B)軸xy?x(C)軸(D)坐標(biāo)原點(diǎn)y2.當(dāng)時，變量（D）是無窮小量0?x(A)(B)x1xxsin(C)(D)x21)ln(?x3.下列等式中正確的是（B）(A)(B)dd()arctan112??xxxdd()12xxx??(C)(D)dd(ln)222xxx?dd(tan)cotxxx?4.下

2、列等式成立的是（A）(A)(B))(d)(ddxfxxfx??)(d)(xfxxf???(C)(D))(d)(dxfxxf??)()(dxfxf??5.下列無窮限積分收斂的是（C）(A)(B)xxd11???xxd11???(C)(D)xxd1134???xxdsin1???二、填空題1.函數(shù)的定義域是24)(2???xxxf)2(]2(??????2.函數(shù)的間斷點(diǎn)是12???xxy1??x3.曲線在處的切線斜率是xxf1)(?)11(

3、21?4.函數(shù)的單調(diào)增加區(qū)間是)1ln(2xy??)0(??5.???xxded2xxde2?三、計(jì)算題（每小題9分，共54分）1.計(jì)算極限解：4586lim224?????xxxxx32)1)(4()2)(4(lim4586lim4224????????????xxxxxxxxxx復(fù)習(xí)資料2.設(shè)，求xxxylncosln2??dy解：由微分運(yùn)算法則得)ln(d)cos(lnd)lncos(lndd22xxxxxxy????)(lnd)

4、(dln)(cosdcos122xxxxxx???xxxxxxxxxd1dln2dcossin2?????xxxxxd)ln2tan(????3.計(jì)算不定積分xxxdcos?解：由換元積分法得cxxxxxx?????sin2)d(cos2dcos4.計(jì)算定積分?e1dlnxxx解：由分部積分法得????e12e12e1)d(ln21ln2dlnxxxxxxx414ed212e2e12?????xx四、應(yīng)用題求曲線yx2?上的點(diǎn)，使其到點(diǎn)