大一上微积分题,写出过程哈……一定加分

2个回答

  • 1.(0,—2)切线斜率为2/3

    y'=3x^2+a 带入x=0,y'=2/3 得a=2/3 即y'=3x^2+2/3

    y=x^3+2/3*x+b 带入(0,—2)得b=-2

    y=x^3+2/3*x-2

    2.=∫(x/f(x))'dx=x/f(x)+C

    3.=x^3/3-1/(3x^3)+x+C

    4.题意不明

    5.题意不明

    6.=∫(x^4-1+2)/(x-1)(x^2+1)dx

    =∫(x+1+1/(x-1)-(x+1)/(x^2+1))dx

    =∫((x+1+1/(x-1)-x/(x^2+1)-1/(x^2+1))dx

    =0.5*x^2+x+ln|x-1|-0.5*ln(x^2+1)-arctanx+C

    7.f(x)/F(x)=F'(x)/F(x)=(lnF(x))' (F(x)>0绝对值去掉)

    =1/(x^2+1)=(arctanx)'

    两边积分 lnF(x)=arctanx+C 由F(0)=1得C=0

    即F(x)=e^arctanx f(x)=e^(arctanx)/(x^2+1)