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).

- Oct 18th 2010, 06:34 PMWorkDayNNightValues 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). - Oct 19th 2010, 03:57 AMHallsofIvy
Have you

**tried**anything? Like writing down the formula for the derivative at 0:

$\displaystyle \lim_{h\to 0}\frac{h^a sin(1/h)- 0}{h}= \lim_{h\to 0}h^{a-1}sin(1/h)$

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.)