电大经济数学基础作业参考答案--(一)
经济数学基础形考作业(一)参考答案
(一)填空题
x1.limx?sin?0. xx?02.设
?x2?1,x?0f(x)???k,x?0?x?1,在x?0处连续,则k?1.
3.曲线y?在(1,2)的切线方程是x?2y?3?0.
24.设函数f(x?1)?x?2x?5,则f?(x)?2x.
?5.设f(x)?xsinx,则f??(π)??. 22(二)单项选择题
1. 当x???时,下列变量为无穷小量的是( D ) A.ln(1?x) B. D.
sinxxx2x?1 C.e
?x21
2. 下列极限计算正确的是( B ) A.limxxx?0?1 B.limx??xxx?0??1
sinxC.limxsin1?1 D.lim?1 xxx?03. 设y?lg2x,则dy?( B ).
1ln101A.21xdx B.xln10dx C.dx D.dx xx4. 若函数f (x)在点x0处可导,则( B )是错误的.
A.函数f (x)在点B.limf(x)?A,但A?f(x)
x?x00x0处有定义
C.函数f (x)在点x0处连续 D.函数f (x)在点x0处可微 5. 若f(1x)?x.,则f'(x)?( B ) A.1x2 B.?1x2 D.?1x (三)解答题 1.计算极限 (1)
x2lim?3x?2x?1x2?1
解:原式?lim(x?1)(x?2)x?1(x?1)(x?1)?limx?21x?1x?1??2 (2)
limx2?5x?6x?2x2?6x?8
解:原式?lim(x?2)(x?3)x?31x?2(x?2)(x?4)?limx?2x?4?2 (3)lim1?x?1x?0x
解:原式?lim(1?x?1)(1?x?1)?xx?0x(1?x?1)?limx?0x(1?x?1)??12
(4)
lim2x2?3x?5x??3x2?2x?4
解:原式?23 C.1x