Lab  2
Your Name Here

Do your work in this notebook.  Submit the work via BLACKBOARD digital dropbox, as described in class and in the instructions available on Professor Goodman's web page.  The title of your submission should be
LastNameInitialLab2.nb,
for example
GoodmanFLab2.nb.

Your assignment:

1.  Use Mathematica to graph the function 
f[x, y] = 
        3  Cos[π x y ] (e^(-((x^2) + (y^2)))) 
and its tangent plane together at (x0,  y0) = (1/5, 1/7). Plot the graphs on several different scales, i.e. in regions of different diameter.

2.Find the approximate change of the function
 f[x, y] = 
        3  Cos[π x y ] (e^(-((x^2) + (y^2)))) 
 as (x,  y)  changes from (x0, y0) = (2,3)  to (1.85,  3.12) , using the tangent plane approximation,

3. Find the directional derivative of the function
 f[x, y] = 
        3  Cos[π x y ] (e^(-((x^2) + (y^2)))) 
 at (x0, y0) = (2,3) in the direction of the increment  (4,  5).

Do this work in a separate notebook. I have provided you with a template notebook called Lab2_report.nb.