浙江师范大学高数试题及答案

PAGE浙江师范大学《高等数学》考试卷Ａ卷一选择题（每小题2分，共16分）1．设函数，则点是函数的()A.极大值点但非最大值点;B.极大值点且是最大值点;C.极小值点但非最小值点;D.极小值点且是最小值点.2．设,则（）A.;B.;C.;D..3．下列表示过轴的平面是()A．；B．；C．；D．.4．设，则I满足()A.B.C.D.5．设,其中由曲线所围成的区域,则（）.A.；B.；C.；D..6．是级数收敛的（）条件A．充分;B．充要;C．必要;D．非充分非必要.7．下列方程中是一阶非齐次线性微分方程的是()．A．; B．;C．; D．.8.若方程的系数满足，则该方程有特解()A.B.C.D.二填空题（每小题2分，共12分）１．二元函数的定义域为=1\*GB3①.２．设则在点的值为②.３．交换二次积分的次序③.４．通解为的微分方程为④.５．幂级数的收敛区间为⑤.６．级数发散时，的取值范围是⑥.三计算题（每小题8分，共56分）1．,求.2．求的极值.3.由方程确定了隐函数,求.4．计算二重积分，其中是由圆周及轴所围成的右半闭区域.5求微分方程满足初始条件的特解.6．计算，其中是顶点分别为，和的三角形区域.7．已知,求的和函数．四、应用题（12分,每小题6分）１．求函数的拉普拉斯变换,并计算积分.２．求由曲面及所围立体的体积.五、综合题（4分)设在点可导，在上连续，又求浙江师范大学《高等数学》考试卷Ａ卷标准答案一选择题（每小题2分，共16分）1D2D3D4A5A6C7D8B二填空题（每小题2分，共12分）=1\*GB3①②③④⑤⑥三计算题（每小题8分，共56分）1．,求.······4分解:······4分····················４分····················４分2．求的极值.······4分解:,解得三个点······4分ABC-404······3分······3分80864···1分由上表可知处取不到极值,取到极小值,···1分3.由方程确定了隐函数,求.······························4分解:令,则有······························4分,······················4分所以······················4分4．计算二重积分，其中是由圆周及轴所围成的右半闭区域.······················4分解:······················4分······················4分······················4分5求微分方程满足初始条件的特解.······3分解:原方程所对应的齐次线性微分方程为,即······3分·······································1分·······································1分解得·························1分则原方程的通解可设为·························1分带入原方程有············3分得到,所以原方程的通解为············3分.6．计算，其中是顶点分别为，和的三角形区域.解:原式………4分……….4分7．已知,求的和函数．······4分解:······4分······································4分······································4分四、应用题（12分,每小题6分）１．求函数的拉普拉斯变换,并计算积分.解.………3分故…….3分２．求由曲面及所围立体的体积.······································4分解:,得,则两曲面所围成的立体的积分区