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Unformatted text preview: ( x ) = (1 + x ) 1 / 3 . a) Find the Taylor polynomial of degree 2, P 2 ,a ( x ), of f expanded about a = 0. b) For the given f use Taylors theorem to write an expression for the error term f ( x )-P 2 , ( x ). c) Show that when x &gt; 0 the error f ( x )-P 2 ,a ( x ) is at most 5 81 x 3 . d) Write a fraction that estimates (1 . 2) 1 / 3 and show that the error in your estimate is at most 1 2025 . 8) Evaluate the following integrals: a) Z x 2 x 3 + 7 dx b) Z / 4 tan d c) Z 1 t ( t-1) dt d) Z x 2 ln x dx e) Z 1 arctan x 1 + x 2 dx f) Z 1 x e-2 x dx 9) Let f ( x ) = Z x cos( t 2 ) dt . a) Find f ( x ). b) Using the known power series for cos x , nd a power series for f (1). c) Use the rst 2 terms of the series to estimate the integral Z 1 cos( t 2 ) dt . Find an upper bound for the error of this approximation....
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