f(x) = e^(-1/x2) if x 不等于0,
f(x) = 0 if x = 0.
a. use the definition of derivative to show that f is differentiable at x = 0. What is f '(0)?
就是要用lim h->0 {[f(x+h)-f(x)]/h} 得出 f '(0)
b. show that lim x->0 [e^(-1/x2)/x^n] = 0 for every positive integern
好的在加分。
不可以用泰勒公式，因为泰勒公式假定极限存在，而题目是要我们证明极限存在a. use the definition of derivative to show that f is differentiable at x = 0. What is f '(0)?利用导数的定义证明f在x=0处可导。f'(0)=?解：f(x) 在x=0处可导 当且仅当 下面两个极限存在并相等：lim h->0+ (f(h)-f(0))/h = lim h->0- (f(h)-f(0))/hlim h->0+ (f(h)-f(0))/h= lim h->0+ e^(-1/h2)/h= lim h->+∞ e^(-h²...
解：对于x=0点的导数，必须用定义式来求解。根据定义， f '(0)=limh→0{[f(0+h)-f(0)]/h}，因为x=0时，f(0)=0,所以，即f '(0)=limh→0[f(h)/h]f(h)=e^(-1/h2)=1/[e^(1/h2)]则f(h)/h=(1/h)/[e^(1/h2)]令1/h...
