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che132a-rec-1 - Plot these functions on the domain[0,3 5...

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Chemical Engineering 132A Analytical Methods of Chemical Engineering Professor Mike Gordon, Fall 2011 Mathematica Assignment #1 If you do not finish during recitation, turn in your completed assignment by Monday, 3 October 2011 . 1) Define the following functions: ( x e x f x 2 cos ) ( 2 - = ) sin( ) ( 3 x x x g - = ( 29 + + = 1 2 3 4 log 2 4 x x x h 2) Evaluate each of these functions at x=2. Give both symbolic and numerical answers. 3) Plot each function on the domain [0,3]. 4) Define 3 new functions which are the derivatives of f, g, and h.
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Unformatted text preview: Plot these functions on the domain [0,3]. 5) Show that: ( 29 ( 29 ( 29 ( 29 x b x a x x u 3 sin 3 cos + = is a general solution to the following ODE by defining ( 29 x u , computing its derivatives, and substituting them back into the ODE. Hint : define the derivatives as functions (say up[x] and upp[x]), then substitute everything into the equation and see if it is equal to zero using the command Simplify . ) 2 9 ( 2 2 2 = + + ′-′ ′ u x u x u x...
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