两个函数的交点

来源：百度知道 编辑：UC知道 时间：2024/06/01 01:49:19
f(x)=e^x与f(x)=-x/0.194+1.0832这两个函数的求交点的具体方法。
像这种指数函数与一次函数的交点问题我老不会，望高手指教一二.....................

求两函数交点，就是两个函数式相等时，方程的解

如题中，即
e^x=-x/0.194+1.0832
解出x值，再求出e^x的值

数对（x,e^x）即为两函数的交点坐标

令e^x= -x/0.194+1.0832,
于是数值解法有两种:
x=㏑(-x/0.194+1.0832),为x取初值,然后反复叠代.
或者
x=(1.0832-e^x)*0.194,为x取初值,然后反复叠代.
这两个表达式中一般会有一个是收敛的,可以求出最终的结果,
下面是用第二个表达式由初值x=0叠代出的结果,有效数字到第八位相同就停止叠代了.
{"叠代次数","x值"},
{1,0.015168370953276203},
{2,0.013175705055455735},
{3,0.013567799896462038},
{4,0.013490709524859437},
{5,0.013505868769086497},
{6,0.013502887909546646},
{7,0.013503474058669173},
{8,0.013503358799839351},
{9,0.01350338146403941},
{10,0.013503377007409579},
{11,0.013503377883749772}
于是交点坐标为:
(x,e^x)=(0.0135033778,1.01359496)

自己求