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Math Help - Values of a for x^a sin(1/x) when x does not equal 0 and (0,0) is a point.

  1. #1
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    Values of a for x^a sin(1/x) when x does not equal 0 and (0,0) is a point.

    i) Determine "a" values for which f is differentiable at 0 and determine the f'(o) values.

    ii) Determine "a" values for which f' is continuous at 0.

    iii) Determine "a" values for which f"(0) exists and determine its value(s).
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  2. #2
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    Have you tried anything? Like writing down the formula for the derivative at 0:
    \lim_{h\to 0}\frac{h^a sin(1/h)- 0}{h}= \lim_{h\to 0}h^{a-1}sin(1/h)
    Does that give you any ideas.

    (I assume that your "and (0, 0) is a point" means that (0, 0) is a point in the graph of y= f(x)- in other words, that f(0)= 0.)
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