醫(yī)學高等數(shù)研習題解答(1,2,3,6)

1、.第一章函數(shù)、極限與連續(xù)習題題解(P27)一、判斷題題解一、判斷題題解1.正確。設h(x)=f(x)f(?x)則h(?x)=f(?x)f(x)=h(x)。故為偶函數(shù)。2.錯。y=2lnx的定義域(0?)y=lnx2的定義域(??0)∪(0?)。定義域不同。3.錯。。故無界。????201limxx4.錯。在x0點極限存在不一定連續(xù)。5.錯。逐漸增大。01lim?????xx6.正確。設，當x無限趨向于x0并在x0的鄰域內(nèi)，有。Axfxx

2、??)(lim0??????AxfA)(7.正確。反證法：設F(x)=f(x)g(x)在x0處連續(xù)，則g(x)=F(x)?f(x)，在x0處F(x)，f(x)均連續(xù)，從而g(x)在x=x0處也連續(xù)，與已知條件矛盾。8.正確。是復合函數(shù)的連續(xù)性定理。二、選擇題題解二、選擇題題解1.??)(22)]([2)()(222Dxfxxxfxxx??????2.y=x(C)3.(A)01sinlim0??xxx4.(B)0cos1sinlim0??

3、xxxx5.(B))1(2)(lim2)3(lim)(lim2)13(lim)(lim11111fxfxxfxxfxxxxx???????????????????6.(D)3092????xx7.畫出圖形后知：最大值是3，最小值是?10。(A)8.設則，連續(xù)，由介質(zhì)定理可知。(D)1)(4???xxxf13)2(1)1(???ff)(xf三、填空題題解三、填空題題解1.?210???x31??x2.是奇函數(shù)，關于原點對稱。)arctan

4、(3xy?3.。31?????62??T4.可以寫成。yx??xy??5.設，，6tx?11??tx3211lim11lim21321?????????ttttttt6.有界，，故極限為0。2arctan??x01lim???xx.6.求函數(shù)的極限(1)原式=。34311311211211lim11?????????nnn(2)原式==。?????????????????????????????????1113121211limnnn?

5、1111lim???????????nn(3)原式==。3211)1(3limxxxx?????112lim)1)(1()2)(1(lim2121????????????xxxxxxxxxx(4)原式=。31323322lim?????????????????nnn(5)原式==。（P289常見三角公式提示）20sin2sin2limxxxx?4sin22sin4lim0????xxxxx(6)原式=，令，則，xxxxxarctanar

6、csinlim210??tx?arcsinxt?sin1sinlimarcsinlim00????ttxxtx令，則，，原式=。tx?arctanxt?tan1cossinlimtanlimarctanlim000???????tttttxxttx21(7)原式===e3。??3tan31202tan31lim???xxx??3tan31202tan31lim????????xxx(8)原式==?=e2。122121221lim????

7、?????????xxx22121221lim?????????????????????xxx11221lim???????????xx(9)原式==。)1sin1(2sin2sinlim20???xxxxxx11sin112sin2sinlim220????????????????xxxxxxx(10)令，則，原式=(填空題11)。axt??tax??atatetee???)1(lim07.，，，?，221233sin21aaaS??