MATH 241 -- Multivariable Calculus
October 23, 2007
The following plots show the graph of a function f(x,y),
together with the graphs of its Taylor polynomials of degree
1 and degree 2. Here is the function f
(1) |
The graph of f alone:
This computes the first degree Taylor polynomial at (a,b) = (0,0):
(2) |
Here is the plot of f and the first degree Taylor polynomial. The
graph of p1 is the tangent plane at (a,b) = (0,0).
This computes the second degree Taylor polynomial at (0,0):
(3) |
The graph of the second degree polynomial alone:
The graphs of f and its second degree Taylor polynomial together.