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Unformatted text preview: sin( x ) sin(2 x ) x 2 + x 4 (c) lim x ln(1 + x ) x 3 3. Find the Maclaurin series (Taylor series at x = 0) for the following functions: (a) f ( x ) = ln(1 + x 2 ) (b) f ( x ) = 1ex x (c) f ( x ) = tan x out to and including terms of order 5 . (d) f ( x ) = e sin x out to and including terms of order 3 . 4 4. Suppose f ( x ) is a function satisfying f (0) = 10 and f ( x ) = 1 1 + x 4 for all x. Compute the linear approximation L to f (0 . 1) and show that L2 105 < f (0 . 1) < L. 5. Suppose f ( x ) is a function which is twice dierentiable for < x < and satises f (0) = f (1) = f (2) = 0 . Show that there exists x such that 0 < x < 2 and f 00 ( x ) = 0 . 5...
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 Winter '06
 denissjerve

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