山東大學(xué)網(wǎng)絡(luò)高起專高等數(shù)學(xué)試題及答案

1、高等數(shù)學(xué)模擬卷高等數(shù)學(xué)模擬卷1一求下列極限求下列極限1=0（有界量乘無窮小量）1limsinnnn??2求=0limxxx?1lim1lim00x????????xxxxx3求=10limxxe?0limlim1010???????xxxxee=0sin4limsin5xxxxx???31616155sin5sinlim55sin5lim5sinsinlimsinlim0000??????????????xxxxxxxxxxxxxxxx

2、xxxxxx（第一個重要極限）二取什么值，連續(xù)a0()0xexfxaxx???????答：根據(jù)函數(shù)在一點(diǎn)處連續(xù)的定義，，)(lim)(lim00xfaxfxx??????而==1)(lim0xfx??xxe??0lim所以a=1三計算下列各題1已知求答：2sinlnyxx??yy’=2(sinxlnx)’=2[(sinx)’(lnx)(sinx)(lnx)’]=2cosxlnx2xsinx2()()xfxyfeey??已知，求答：由鏈?zhǔn)?/p>

3、法則，????????dxdyeefeeefdxxfxxfxx???dy所以????????xfxxfxxeefeefy???123xxedx?求1111.[ln(ln)]..[ln(ln)][ln(ln)]lnyxxxxx???2yxxyy?求lnln.ln.ln1.lnln..lnlnlnlnyxxyyxxyyyxyyxxyxyyxyyxyyxyxxy?????????????????????解：2220100coslimsinxx

4、xtdtx???四求由于分子分母極限都為0，所以可以對分子分母分別求導(dǎo)，得到Lim(2x2xcosx^4)10sin^9(x)cosx再對兩邊求導(dǎo)五求和所圍平面圖形的面積225yx??4yx???????225423233113173511316422623yxyxysydyyyy???????????????解：得交點(diǎn)，，六22(1)24dyxxyxdx???2222222()ln1122323224(1)(1)(1)1()4443(