數(shù)學(xué)分析3期末練習(xí)題三參考答案

1、110統(tǒng)計專業(yè)和數(shù)學(xué)專業(yè)數(shù)學(xué)分析（3）期末練習(xí)題三參考答案1.試求極限.42lim)00()(xyxyyx???解()(00)()(00)24limlim(24)xyxyxyxyxyxyxy???????()(00)11lim424xyxy?????.2.試求極限.)()cos(1lim222222)00()(yxyxeyxyx????解由222222222222222()(00)()(00)22sin1cos()2limlim()4(

2、)2xyxyxyxyxyxyxyxyxyee??????????1002???.3.試求極限.1sin1sin)(lim)00()(yxyxyx??解由于()(00)()(00)111111lim()sinsinlim(sinsinsinsin)xyxyxyxyxyxyxy?????又2yx?所以()(00)11limsinsin0xyxxy??，()(00)11limsinsin0xyyxy??所以()(00)11lim()sinsi

3、n0xyxyxy???.4.試討論.lim422)00()(yxxyyx??解當(dāng)點沿直線趨于原點時，)(yxxy?232424000limlim0xxyxxyxxyxx????????.當(dāng)點沿拋物線線趨于原點時，)(yx2yx?22424440001limlim2yyxyxyyxyyy????????.因為二者不等，所以極限不存在.3得22()52(1)(1)(2)(2)fxyxxyy????????.10.求函數(shù)的極值.)2()(22

4、yyxeyxfx???解由于222222(2)(22)0xxxxfexyyeexyy?????????22(1)0xyfey???解得駐點，)11(??222222(22)(22)2xxxxxxyxyyfexyyefeyfe????????22(11)0(11)0(11)2xxxyyyAfeBfCfe??????????????2200ACBA????所以是極小值點極小值為)11(??.2)11(2?????ef11.敘述隱函數(shù)的定義.

5、答:設(shè)，，函數(shù)對于方程若存在集合RX?RY?.:RYXF??0)(?yxF與，使得對于任何，恒有唯一確定的，使得滿足方程XI?YJ?Ix?Jy?()xy則稱由方程確定了一個定義在上，值域含于的隱函數(shù)隱函數(shù)。一0)(?yxF0)(?yxFIJ般可記為且成立恒等式)(xfy?.JyIx??(())0.FxfxxI??12.敘述隱函數(shù)存在唯一性定理的內(nèi)容.答:若滿足下列條件:()Fxy（i）函數(shù)F在以為內(nèi)點的某一區(qū)域上連續(xù)0P)(00yx2R