Approximation Consider the following approximations for a function f(x, y) centered at (0, 0).
Linear Approximation:
Quadratic Approximation:
Note that the linear approximation is the tangent plane to the surface at (0, 0, f (0, 0)).]
(a) Find the linear approximation of
(b) Find the quadratic approximation of
(c) When
(d) Complete the table.
x 
y 
f(x, y) 


0 
0 

0 
0.1 

0.2 
0.1 

0.2 
0.5 

1 
0.5 
(e) Use a computer algebra system to graph the surfaces
(a)
To calculate: The linear approximation of the function
Given:
The provided function is:
Formula used:
The linear approximation of a function
Calculation:
Consider the provided function,
The partial derivatives of this function with respect to
And,
So, the partial derivatives of the function at
(b)
To calculate: The quadratic approximation of the function
(c)
The function obtained by the tailor polynomial on putting
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