内容发布更新时间 : 2024/11/13 7:26:47星期一 下面是文章的全部内容请认真阅读。

?1,|x|?131.设函数f(x)??, 则f(sinx)?_________.

?0,|x|?1解：|sinx|?1?f(sinx)?1.

1?x?3?=_____________.

x?2x2?2x1?x?3(x?2)1解：lim?lim?lim? 2x?2x?2x?2x?2xx(x?2)(x?1?3)x(x?1?3)32.lim3. 1243 33.设函数y?arctan2x，则dy?__________.

2解：dy?dx . 21?4x34.设函数f(x)?x3?ax2?bx在x??1处取得极小值-2，则常数a和b分别为___________.

解：f?(x)?3x2?2ax?b?3?2a?b?0,?2??1?a?b?a?4,b?5.

??35.曲线y?x3?3x2?2x?1的拐点为 __________.

解：y??3x2?6x?2?y???6x?6?0?(x,y)?(1,?1) .

36.设函数f(x),g(x)均可微，且同为某函数的原函数，有f(1)?3,g(1)?1 则f(x)?g(x)?_________.

解：f(x)?g(x)?C?C?f(1)?g(1)?2?f(x)?g(x)?2.

37.?(x2?sin3x)dx? _________.

??1?解：?(x?sinx)dx??xdx??sinxdx?2????????23?2?3?02?3xdx?0?.

32x?2?e,x?038.设函数f(x)??2 ，则 ?f(x?1)dx?__________.

0??x,x?0x?1?t210122解：?f(x?1)dx?????f(t)dt??xdx??exdx?e? .

0?1?103??39. 向量a?{1,1,2}与向量b?{2,?1,1}的夹角为__________.

??????a?b31?解：cos?a,b????????a,b?? .

3|a||b|662?y2?2x40.曲线L：绕x轴旋转一周所形成的旋转曲面方程为 _________. ??z?0解：把y2?2x中的y2换成z2?y2，即得所求曲面方程z2?y2?2x.

?2z?_________. 41.设函数z?xy?xsiny ，则

?x?y2?2z?z?1?2xcosy. ?y?2xsiny?解：

?x?y?x42.设区域D?{(x,y)|0?x?1,?1?y?1}，则??(y?x2)dxdy?________.

D