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52 10) Normal[ Series[Tan[x],{x,0,3}]] followed by Normal[ Series[Tan[x],{x,0,5}]] followed by Normal[ Series[Tan[x],{x,0,10}]] followed by %%% /. x->1/2 followed by %%% /. x->1/2 followed by %%% /. DSolve[{y [x]+y[x]==0,y[0]==3,y’[0]==2},y[x],x])[[1]] The y[x]/. command tells Mathematica to replace y[x] with the solution from DSolve[ ] - but this is a list, so the [[1]] at the end returns the first (and only) element of the list. {-2,1,0,3} For 3-8, define a={{1,2,3},{4,5,6},{2,1,5}} and b={{3,2,1},{0,-6,5},{1,2,3}}.

The following picture is the result of evaluating the command Plot3D[f,{x,-6,6},{y,-6,6},PlotRange->All,BoxRatios ->{2,1,1}]. Notice how the scales at the base of the graph have been distorted - the x-axis is now twice as large as the y-axis. The viewpoint you look at the surface from: In all of the 3-D plots generated so far, the vantage you view the surface from is the same - you are viewing the surface from a point which is 44 above the fourth quadrant of the xy-plane (this is much easier to figure out if you label the axes using AxesLabel).

5) Create a plot of the curve defined by x=sin(t), y=cos(t), z=sin( 2t) as t goes from 0 to 10π. Label the axes and make Mathematica sample enough points to get a smooth curve. 6) Create a plot of the surface defined by x = and v goes from 1 to 9. sin(u) √ ,y v = cos(2u), z = v as u goes from 0 to 2π 49 Solutions to Exercises The answers to the exercises are given as a Mathematica command or sequence of commands. If a problem takes more than one command, “followed by” or “and” indicate the sequence of commands.

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