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FJU 發問時間： 科學數學 · 10 年前

# 高等微積分（The Derivative)

2 個已更新項目:

### 1 個解答

• 10 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.