设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0.证明:在(a,b)内至少存在一点c,使f'(c)+df(c)=0这d为任意实数.
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/06 11:52:15
![设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0.证明:在(a,b)内至少存在一点c,使f'(c)+df(c)=0这d为任意实数.](/uploads/image/z/6974053-61-3.jpg?t=%E8%AE%BEf%28x%29%E5%9C%A8%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%28a%2Cb%29%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94f%28a%29%3Df%28b%29%3D0.%E8%AF%81%E6%98%8E%EF%BC%9A%E5%9C%A8%EF%BC%88a%2Cb%EF%BC%89%E5%86%85%E8%87%B3%E5%B0%91%E5%AD%98%E5%9C%A8%E4%B8%80%E7%82%B9c%2C%E4%BD%BFf%27%28c%29%2Bdf%28c%29%3D0%E8%BF%99d%E4%B8%BA%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0.)
x͑J@m ɋBҚ$KUI[tӤR4?mU^;3-(Z7a8s2;^KKjxG2TFEB@TgI,$R/ՠW#tViUzr>L8[4eVMj_M)aF1Mչxu?QpxOqH6h`_j{[?
yۂ!xkbG_جM9[!p&^{7)2f#~"ƛo8Xv(5,uzL`u7OB1uOQz
设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0.证明:在(a,b)内至少存在一点c,使f'(c)+df(c)=0这d为任意实数.
设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0.证明:在(a,b)内至少存在一点c,使f'(c)+df(c)=0这
d为任意实数.
设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0.证明:在(a,b)内至少存在一点c,使f'(c)+df(c)=0这d为任意实数.
设g(x)=f(x)e^(dx),
由题意得g(x)在(a,b)上可导,[a,b]内连续,
又g(a)=f(a)e^(da)=0
g(b)=f(b)e^(da)=0
即g(a)=g(b)
对g(x)在[a,b]区间应用罗尔定理,
至少存在一点c,使得
g'(c)=0
即f'(c)e^(dc)+df(c)e^(dc)=0
对上式左右除以e^(dc)可得
原命题得证.
设f(x)在[a,b]上连续,且a
设函数f(x)在[a,b]上连续,a
设f(x)在[a,b]上连续,且a
设f(x)在[a,b]上连续,且a
设f(x)在[a,b]上连续,a
设函数f(x)在[a,b]上连续,a
设函数f(x)在[a,b]上连续,在(a,b)内可导且f'(x)
设函数f(x)在[a,b]上连续,在(a,b)上可导且f'(x)
证明:设f(x)在[a,b]上连续,在(a,b)内可导,(0
设f(x)在[a,b]上连续,在(a,b)上可导(0
设函数f(x)在[a,b]上连续,在(a,b)内可导(0
设f(x)在[a,b]上连续,在(a,b)内可导,(0
设f(x)在[a,b]上连续,在(a,b)内可导(0
设f(x)在[a,b]上连续,在(a,b)内可导(0
设函数f(x),g(x)在区间[a,b]上连续,且f(a)
证明设f(x)在有限开区间(a,b)内连续,且f(a+) ,f(b-)存在,则f(x)在(a,b)上一致连续.
设函数f 在[a,b]上连续,M=max|f(x)|(a
【50分高数微积分题】设f(x)在[a,b]上连续,在(a,b)内可导 f(a)f(b)>0 f(a)f[(a+b)/2]