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Unformatted text preview: x = 0 of the function f ( x ) = tan(2 | x | + x ) . 6. The function f ( x ) is dened 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 non-zero x . Using only the , de-nition of dierentiation prove that f is dierentiable at x = 0 and nd its derivative at that point. Sketch the graph of the derivative. Is the derivative continuous at x = 0? 7. Let g ( x ) = e-1 /x 2 if x 6 = 0 and g (0) = 0. Calculate the rst two derivatives of g ( x ) at x = 0. Explain your answer! 1...
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This document was uploaded on 01/31/2011.
- Spring '09