设函数y=y(x)由确定,则y=y(x)在x=ln2处的法线方程为________.

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问题 设函数y=y(x)由确定,则y=y(x)在x=ln2处的法线方程为________.

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答案[*]

解析 当x=ln2时,t=±1;当t=±1时,y=0.
(1)当t=-1时,由=-1,
0xeu2du+∫t21arcsinudu=0两边对t求导数得ey2-2tarcsint2=0,
,则法线方程为y=(x-ln2);
(2)当t=1时,由=1.
0yeu2du+∫t21arcsinudu=0两边对t求导得ey2 2tarcsint2=0.
,法线方程为y=(x-ln2),
即法线方程为y=(x-ln2).
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