浙江師范大學(xué)高數(shù)試題及答案

PAGE浙江師范大學(xué)《高等數(shù)學(xué)》考試卷Ａ卷一選擇題（每小題2分，共16分）1．設(shè)函數(shù)，則點(diǎn)是函數(shù)的()A.極大值點(diǎn)但非最大值點(diǎn);B.極大值點(diǎn)且是最大值點(diǎn);C.極小值點(diǎn)但非最小值點(diǎn);D.極小值點(diǎn)且是最小值點(diǎn).2．設(shè),則（）A.;B.;C.;D..3．下列表示過軸的平面是()A．；B．；C．；D．.4．設(shè)，則I滿足()A.B.C.D.5．設(shè),其中由曲線所圍成的區(qū)域,則（）.A.；B.；C.；D..6．是級(jí)數(shù)收斂的（）條件A．充分;B．充要;C．必要;D．非充分非必要.7．下列方程中是一階非齊次線性微分方程的是()．A．; B．;C．; D．.8.若方程的系數(shù)滿足，則該方程有特解()A.B.C.D.二填空題（每小題2分，共12分）１．二元函數(shù)的定義域?yàn)?1\*GB3①.２．設(shè)則在點(diǎn)的值為②.３．交換二次積分的次序③.４．通解為的微分方程為④.５．冪級(jí)數(shù)的收斂區(qū)間為⑤.６．級(jí)數(shù)發(fā)散時(shí)，的取值范圍是⑥.三計(jì)算題（每小題8分，共56分）1．,求.2．求的極值.3.由方程確定了隱函數(shù),求.4．計(jì)算二重積分，其中是由圓周及軸所圍成的右半閉區(qū)域.5求微分方程滿足初始條件的特解.6．計(jì)算，其中是頂點(diǎn)分別為，和的三角形區(qū)域.7．已知,求的和函數(shù)．四、應(yīng)用題（12分,每小題6分）１．求函數(shù)的拉普拉斯變換,并計(jì)算積分.２．求由曲面及所圍立體的體積.五、綜合題（4分)設(shè)在點(diǎn)可導(dǎo)，在上連續(xù)，又求浙江師范大學(xué)《高等數(shù)學(xué)》考試卷Ａ卷標(biāo)準(zhǔn)答案一選擇題（每小題2分，共16分）1D2D3D4A5A6C7D8B二填空題（每小題2分，共12分）=1\*GB3①②③④⑤⑥三計(jì)算題（每小題8分，共56分）1．,求.······4分解:······4分····················４分····················４分2．求的極值.······4分解:,解得三個(gè)點(diǎn)······4分ABC-404······3分······3分80864···1分由上表可知處取不到極值,取到極小值,···1分3.由方程確定了隱函數(shù),求.······························4分解:令,則有······························4分,······················4分所以······················4分4．計(jì)算二重積分，其中是由圓周及軸所圍成的右半閉區(qū)域.······················4分解:······················4分······················4分······················4分5求微分方程滿足初始條件的特解.······3分解:原方程所對(duì)應(yīng)的齊次線性微分方程為,即······3分·······································1分·······································1分解得·························1分則原方程的通解可設(shè)為·························1分帶入原方程有············3分得到,所以原方程的通解為············3分.6．計(jì)算，其中是頂點(diǎn)分別為，和的三角形區(qū)域.解:原式………4分……….4分7．已知,求的和函數(shù)．······4分解:······4分······································4分······································4分四、應(yīng)用題（12分,每小題6分）１．求函數(shù)的拉普拉斯變換,并計(jì)算積分.解.………3分故…….3分２．求由曲面及所圍立體的體積.······································4分解:,得,則兩曲面所圍成的立體的積分區(qū)