Unformatted text preview: x = 0 of the function f ( x ) = tan(2  x  + x ) . 6. The function f ( x ) is deﬁned for all x ∈ R by f ( x ) = ( x 2 (sin(1 /x ) if x 6 = 0 otherwise. Calculate the derivative of f ( x ) at all nonzero x . Using only the ε,δ deﬁnition of diﬀerentiation prove that f is diﬀerentiable at x = 0 and ﬁnd its derivative at that point. Sketch the graph of the derivative. Is the derivative continuous at x = 0? 7. Let g ( x ) = e1 /x 2 if x 6 = 0 and g (0) = 0. Calculate the ﬁrst two derivatives of g ( x ) at x = 0. Explain your answer! 1...
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 Spring '09
 Calculus, Derivative, Continuous function, EXERCISE SHEET

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