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Check the dierentiability of each of the functions below at x0 = 0. (a) f(x) =...

Check the dierentiability of each of the functions below at x0 = 0.

(a) f(x) = x|x|

(b) f(x) = xsinx−1 (f(0) = 0)

(c) f(x) = x2 sinx−1 (f(0) = 0)

(d) f(x) = x2, if x rational 0, if x irrational

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