By Moretti C.

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Use tick marks 0, π2 , π, 3π 2 , 2π on the x-axis and 0, 2 , 1 on the y-axis. Label the plot “y=cos(x)”. 4) Plot y= x31−x from x=-5 to 5. Restrict the range of y-values displayed to -5 to 5. √ 5) Create a plot of y= 9 − x2 as x goes from -3 to 3. Use AspectRatio->Automatic and label both axes. 6) Create a plot of the parametric curve defined by x=t cos(t), y=t sin(t) as t goes from 0 to 10. Use AspectRatio->Automatic, and have Mathematica sample the functions 50 times to create the plot. 7) Create a plot of the curve defined by x=sin(2t), y=sin(t) as t goes from 0 to 20.

6) Create a plot of the parametric curve defined by x=t cos(t), y=t sin(t) as t goes from 0 to 10. Use AspectRatio->Automatic, and have Mathematica sample the functions 50 times to create the plot. 7) Create a plot of the curve defined by x=sin(2t), y=sin(t) as t goes from 0 to 20. 8) Create a graph of the ellipse x2 9 + y2 4 = 1 as x goes from -4 to 4. Preserve the shape of the graph. 9) Create an plot of the curve y 2 = x3 − 16x as x goes from -20 to 20. Label the axes of the plot. 10) Plot the solution to the initial value problem y = 2y − y 2 , y(0) = showing y-values from 0 to 3.

This option is important for “zooming” in on certain features of the graph. For example, if a graph has a vertical asymptote (like tan(x) and 1/x do), Mathematica may try to plot very large ranges for y, say y going from -1000 to 1000. This scale will make it impossible to see any local details on the graph. The graph may have a local maximum at (2,3), but you’ll never see it on that scale. Restricting the range of y-values will allow you to see more features of the graph. An example of this option would be Plot[Sin[x],{x,0,2Pi},PlotRange->{0,1}], which generates the graphic You can also force Mathematica to try to plot all y-values that occur in a graph (sometimes a graph might be “beheaded” by the edges of the plot) - to do this, use PlotRange->All.

### A brief introduction to Mathematica by Moretti C.

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