作业帮一道数学题（英文的）!关于(The derivatives)1.Let f(x)=2x^2-x a.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,compute f'(2).h→0 b.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,find f'(x).h→0 c.Does the formula in part(b)yield the corr
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![一道数学题（英文的）!关于(The derivatives)1.Let f(x)=2x^2-x a.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,compute f'(2).h→0 b.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,find f'(x).h→0 c.Does the formula in part(b)yield the corr](/uploads/image/z/10255811-59-1.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%EF%BC%88%E8%8B%B1%E6%96%87%E7%9A%84%EF%BC%89%21%E5%85%B3%E4%BA%8E%28The+derivatives%291.Let+f%28x%29%3D2x%5E2-x+a.Using+the+definition+f%27%28x%29%3Dlim+%5Bf%28x%2Bh%29-f%28x%29%5D%2Fh%2Ccompute+f%27%282%29.h%E2%86%920+b.Using+the+definition+f%27%28x%29%3Dlim+%5Bf%28x%2Bh%29-f%28x%29%5D%2Fh%2Cfind+f%27%28x%29.h%E2%86%920+c.Does+the+formula+in+part%28b%29yield+the+corr)
一道数学题（英文的）!关于(The derivatives)1.Let f(x)=2x^2-x a.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,compute f'(2).h→0 b.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,find f'(x).h→0 c.Does the formula in part(b)yield the corr
一道数学题（英文的）!关于(The derivatives)
1.Let f(x)=2x^2-x
a.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,compute f'(2).
h→0
b.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,find f'(x).
h→0
c.Does the formula in part(b)yield the correct value of the derivative in part(a)?
d.Using the derivative formula f'(a)= [f(x+h)-f(a)]/(x-a),compute f'(a).How does this compare
x→a
with part(b)?
一道数学题（英文的）!关于(The derivatives)1.Let f(x)=2x^2-x a.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,compute f'(2).h→0 b.Using the definition f'(x)=lim [f(x+h)-f(x)]/h,find f'(x).h→0 c.Does the formula in part(b)yield the corr
1、设f(x)=2x^2-x
a.使用（导数的）定义：f'(x)=lim [f(x+h)-f(x)]/h,计算f'(2):
h→0
f'(2)=lim [f(2+h)-f(2)]/h=lim[2(2+h)^2-(2+h)-(2*2^2-2)]/h
h→0 h→0
=lim[8+8h+2h^2-2-h-6]/h=lim[2h^2+7h]/h=lim[2h+7]=7
h→0 h→0 h→0
b.使用（导数的）定义：f'(x)=lim [f(x+h)-f(x)]/h,求出f'(x):
h→0
f'(x)=lim[2(x+h)^2-(x+h)-(2x^2-x)]/h=lim[2x^2+4hx+2h^2-x-h-2x^2+x]/h
h→0 h→0
=lim[4hx+2h^2-h]/h=lim[4x+2h-1]=4x-1
h→0 h→0
c.(上面）b部分得到的公式,产生了a部分求出的导数的正确值了吗?
x=2代入上面求出的f'(x)得：f'(2)=4*2-1=7.
不错.
d.使用导数公式f'(a)=lim [f(x)-f(a)]/(x-a),计算f'(a),与上面b部分比怎么样?注意：题目中给出的
x→a
公式是错误的.
f'(a)=lim[2x^2-x-(2a^2-a)]/(x-a)=lim[2(x^2-a^2)-(x-a)]/(x-a)=lim[2(x+a)-1]=2(a+a)-1=4a-1;
x→a x→a x→a
比较：设x-a=h,x=a+h,代入上面的公式,与b没有区别.
在b的公式中,让x=a,结果一样.
a.答案是7，就是求f(x)在2处的极限。
b.答案是4x-1，求得的是导函数
c.符合
这三题是通常意义上的导函数及其定义求法
d.根据极限定义和给出的新定义按式进行推导，结果为2x+2a-1
f'(x) = 4x - 1，f'(2) = 7；无论哪种定义都是一样的。
这个好像是对二次函数f(x)=2x^2-x 用导数的定义求导函数值和导函数。