用二分法求方程的近似解(V)

3.1.2用二分法求方程的近似解 知识探究（一）:二分法的概念思考1:有16个大小相同的小球，其中有15个小球质量相等，另有一个小球稍重，用天平称几次就可以找出这个稍重的球？思考2:已知函数在区间（2，3）内有零点，你有什么方法求出这个零点的近似值？(精确到0.01） xf(x)=ln(x)+2x-62-1.3068528192.01-1.2818652782.02-1.2569024892.03-1.2319642072.04-1.2070501922.05-1.1821602072.06-1.1572940172.07-1.1324513932.08-1.1076321062.09-1.0828359342.1-1.0580626552.11-1.0333120532.12-1.0085839112.13-0.983878022.14-0.9591941712.15-0.934532158xf(x)=ln(x)+2x-62.16-0.9098917782.17-0.8852728322.18-0.8606751232.19-0.8360984562.2-0.811542642.21-0.7870074842.22-0.7624928042.23-0.7379984152.24-0.7135241342.25-0.6890697842.26-0.6646351872.27-0.6402201692.28-0.6158245572.29-0.5914481822.3-0.5670908772.31-0.542752475 xf(x)=ln(x)+2x-62.32-0.5184328142.33-0.4941317322.34-0.4698490712.35-0.4455846722.36-0.4213383812.37-0.3971100452.38-0.3728995122.39-0.3487066342.4-0.3245312632.41-0.3003732522.42-0.276232462.43-0.2521087432.44-0.2280019612.45-0.2039119752.46-0.179838652.47-0.155781849xf(x)=ln(x)+2x-62.48-0.131741442.49-0.107717292.5-0.0837092682.51-0.0597172472.52-0.0357410982.53-0.0117806972.540.0121640812.550.0360933592.560.0600072582.570.0839058992.580.1077893992.590.1316578762.60.1555114452.610.1793502212.620.2031743182.630.226983846 xf(x)=ln(x)+2x-62.640.2507789172.650.274559642.660.2983261232.670.3220784722.680.3458167952.690.3695411942.70.3932517732.710.4169486352.720.440631882.730.4643016092.740.487957922.750.5116009122.760.535230682.770.558847322.780.5824509282.790.606041596xf(x)=ln(x)+2x-62.80.6296194172.810.6531844832.820.6767368852.830.7002767122.840.7238040522.850.7473189942.860.7708216252.870.794312032.880.8177902942.890.8412565022.90.8647107372.910.8881530812.920.9115836162.930.9350024232.940.9584095812.950.98180517 思考3:怎样计算函数在区间（2，3）内精确到0.01的零点近似值？区间（a，b）中点值mf（m）的近似值精确度|a-b|（2，3）2.5-0.0841（2.5，3）2.750.5120.5（2.5，2.75）2.6250.2150.25（2.5，2.625）2.56250.0660.125（2.5，2.5625）2.53125-0.0090.0625（2.53125，2.5625）2.5468750.0290.03125（2.53125，2.546875）2.53906250.010.015625（2.53125，2.5390625）2.535156250.0010.007813 思考4:上述求函数零点近似值的方法叫做二分法，那么二分法的基本思想是什么？对于在区间[a，b]上连续不断且f(a)·f(b)