Math 3298  -  Hampton  -  Lab 2  -  Due 10/5

Lab reports should conform to the guidelines explained on the handout.  Collaboration during the lab is strongly encouraged, although the write-up of the lab report must be done individually.

Linearizations and differentiability

Exercises

1.  The modern formula for the windchill temperature at a temperature T in Fahrenheit and wind velocity V in miles/hour is given by 
	WindChillTemp[T_,V_]:=35.74+.6215 T-35.75 V^(.16)+.4275 T V^(.16)
	a. Plot the graph of this function over an appropriate domain.
	b. Find the linearization of the function at the point T = 32 and V = 3.  Graph the linearization together with the original function with the Plot3D function.  Also graph the difference between the linearization and the original function.
	
2. Use the ContourPlot function to draw some level curves of the function f[x_,y_]:=Sin[(x^2+1)/(x^2+y^2)^(C)] for different values of C.  When is this function differentiable at the origin?

In exercise 2, you may want to increase the accuracy of your plots with the PlotPoints or Contours options.  For example, here are some contour plots of the same function:

ContourPlot[  x^3 y  +  
        Sin[1/(x^2  +  1/1000)]/100, {x, -1, 2}, {y, -1, 
        2}]
ContourPlot[ 
      x^3 y  +  Sin[1/(x^2  +  1/1000)]/100, {x, -1, 
        2}, {y, -1, 2}, PlotPoints -> 100, 
      Contours -> {-1, 0, 1}]
ManyContours = 
        Table[i, {i, -17, 17,  .1}];
ContourPlot[ 
      x^3 y  +  Sin[1/(x^2  +  1/1000)]/100, {x, -1, 
        2}, {y, -1, 2}, PlotPoints -> 100, 
      Contours -> ManyContours]