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FJU 發問時間: 科學數學 · 10 年前

高等微積分(The Derivative)

高等微積分(The Derivative)




高等微積分(Uniform Continuity)

高等微積分(Limits of Functions)(上)

高等微積分(Limits of Functions)(下)

2 個已更新項目:

高等微積分(Monotone and Inverse)

1 個解答

  • 10 年前

    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.