高等微積分（Limits of Functions）（上）
高等微積分（Limits of Functions）（下）
高等微積分（Monotone and Inverse)
- no nicknameLv 510 年前最佳解答
1. 這題目就是著名的 differentiable but not C^1的例子。
if x is not zero, then f ' (x) =2x sin(1/x) - cos(1/x)
when x ->0 the limit does not exist. so the left hand side not exist
2. by definition f(-x) =f(x) (because f is even function)
derivative both side - f '(-x) = f '(x) this is exactly the definition of odd fucion. so f ' is odd.
3. cheeck right function and left function eqaul or not when differentiate at x=0
left f '(0)=3, right f ' =2x+3 put x=0 in. they equal.
so f is differentiable at 0
4. the same thing in 3.
if x is not 0 compute the f ' and put 0 in.
I can not read your function when x is not zero.
please do the calculation by yourself.