2. For parts (b) and (c) of this question you will need to use symbolic algebra

Question

2. For parts (b) and (c) of this question you will need to use symbolic algebra software such as MATHEMATICA or Maple. (a) Characterize and sketch, by hand, several level curves of the following functions (i) f(x,y)=x2+y2 (ii) f(x, y) 14 (iii) f(x,y)=x2+y r2 +y?-1 (w+1)2 (iv) f(x,y)= ry (v) f(x,y) = V (b) Use the contour plotting command on the functions in part (a) and compare with the pictures you produced in part (a). (c) Use the 3D plotting command to generate representations of the graphs of the functions in part (a).

Explanation / Answer

Mathematica Code:

f1=((x^2)+(y^2))/(x*y);

f2=y/((x^2)+(y^2)+1);

f3=((x^2)-(y^2))/((x^2)+(y^2));

f4=((x^2)+(y^2)-1)/((x^2)+((y+1)^2));

f5=((1+2*y-x^2)/((y^2)+y))^0.5;

ContourPlot[f1,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot[f2,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot[f3,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot[f4,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot[f5,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot3D[f1,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot3D[f2,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot3D[f3,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot3D[f4,{x,xmin,xmax},{y,ymin,ymax}]

ContourPlot3D[f5,{x,xmin,xmax},{y,ymin,ymax}]

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