Question

lnx=1/x求解

Answer 1

解方程lnx=1/x
解：由于ln1=0<1；ln2=0.6931>1/2=0.5；故解在区间(1，2)内。这是超越方程，只能用数字解法
求其近似值。为此列表：
x........................lnx..............1/x
1.5................0.4054..........0.6666
1.8................0.5878..........0.5555
1.7................0.5306..........0.5882
1.75..............0.5596..........0.5714
1.78..............0.5766..........0.5618
1.77.............0.5710...........0.5650
1.765...........0.5682...........0.5657
1.764...........0.5676...........0.5669
1.762...........0.5664...........0.5675
1.763...........0.5670............0.5672
1.7635.........0.5673............0.5671
1.76332......0.567198........0.567112
取x=1.76332，绝对误差<0.0001；希望精度再高点，可继续试求。

Answer 2

设f(x)=lnx-1/x,x>0,则
f'(x)=1/x+1/x^>0,
∴f(x)↑，
f(x)=0只有1个根，
f(1.8)≈0.03，f(1.7)≈-0.05，
∴所求的解约为1.8.

Answer 3

移项求导，解方程，找零点