高数题求解答

Question

最好能拍下解题步骤来，最好别只给答案，谢谢啦

Answer 1

1、把x=3代入，得：0
2、lim(x²-3x+2)/(x-1)=lim(x-1)(x-2)/(x-1)=lim(x-2)=-1
3、lim(x²-5x+6)/(x²-9)=lim(x-2)(x-3)/[(x+3)(x-3)]=lim(x-2)/(x+3)=1/6
4、lim(x²+2x-3)/(x²-1)=lim(x-1)(x+3)/[(x-1)(x+1)]=lim(x+3)/(x+1)=2
5、y=x³+cosx y'=3x²-sinx
6、y=x³+3^x+e³ y'=3x²+3^xln3
7、y=3^x+lnx+arctan3 y'=3^xln3+1/x
8、y=arctanx+x²e^x+ln2 y'=1/(1+x²)+2xe^x+x²e^x
9、y=e^x+sinx dy=e^xdx+cosxdx
10、y=lncosx dy=(1/cosx)(-sinx)dx=-tanxdx
11、∫(e^x+cosx)dx=e^x+sinx+C
12、∫(3e^x-2cosx)dx=3e^x-2sinx+C
13、∫<-1,1>(x³+1/(1+x²))dx=(1/4)x^4+arctanx|<-1,1>=π/2
14、∫<0,π/2>xsinxdx=-∫<0,π/2>xdcosx=-xcosx+∫<0,π/2>cosxdx
=-xcosx+sinx|<0,π/2>
=1