(x+h)^(1/3)如何解 急啊
来源:百度知道 编辑:UC知道 时间:2024/05/18 03:32:52
题目中让我先证明 a-b={a^(1/3)-b^(1/3)}{a^(2/3)+a^(1/3)b^(1/3)+b^(2/3)}
第二问让我根据这个证明来求 d/dx x^(1/3)
要求用first principles
就是这个公式limit {f(x+h)-f(x)}/h
要怎么做啊?
第二问让我根据这个证明来求 d/dx x^(1/3)
要求用first principles
就是这个公式limit {f(x+h)-f(x)}/h
要怎么做啊?
a-b={a^(1/3)-b^(1/3)}{a^(2/3)+a^(1/3)b^(1/3)+b^(2/3)}
这就是立方差
x^3-y^3=(x-y)(x^2+xy+y^2)
a-b={a^(1/3)-b^(1/3)}{a^(2/3)+a^(1/3)b^(1/3)+b^(2/3)}
所以a^(1/3)-b^(1/3)=(a-b)/{a^(2/3)+a^(1/3)b^(1/3)+b^(2/3)}
[(x+h)^(1/3)]^3=x+h
[x^(1/3)]^3=x
所以 {f(x+h)-f(x)}/h
=[(x+h)^(1/3)-x^(1/3)]/h
={[(x+h)-x]/[(x+h)^(2/3)+(x+h)^(1/3)x^(1/3)+x^(2/3)]}/h
={h/[(x+h)^(2/3)+(x+h)^(1/3)x^(1/3)+x^(2/3)]}/h
=1/[(x+h)^(2/3)+(x+h)^(1/3)x^(1/3)+x^(2/3)]
h→0
所以极限=1/[x^(2/3)+x^(1/3)*x^(1/3)+x^(2/3)]
=1/[3x^(2/3)]
即(1/3)x^(-2/3)
若函数f(x)=1/1+x时f(x+h)-f(x)=?
若函数f(x)在点x=a处可导,则lim(h→0)[f(a+4h)-f(a-2h)]/3h=?
已知抛物线y=a(x-h)(x-h)+K的顶点为(2,-3),且过点(-1,6),求a ,h , k
如何解2/x>x+1?
2x^3-hx+k能被(x+2)和(x-1)整除,求2h-3k
方程(x+1/x+2)+(x+2/x+3)=(x+3/x+4)+(x+4/x+5)的解
(x+2/x+1)+ (x+6/x+5)=(x+3/x+2)+(x+5/x+4)怎么解?
分式方程问题:解方程:[x+1)/(x+2)]+[(x+6)/(x+7)]=[(x+2)/(x+3)]+[(x+5)/(x+6)]
3.ax^3+bx^2+cx+d能被x^2+h^2(h=/=0)整除,
3.ax^3+bx^2+cx+d能被x^2+h^2(h=/=0)整除,证明