🟡11 - Linearization (Linear Approximation) of Multivariable Functions

So after finding the equation of the tangent plane to the surface at a point xo,yo, we are going to learn how to use this to approximate the function f(x,y).

The linearization of a function is given by
L(x,y) = f(xo,yo) + fx(xo,yo)(x-xo) + fy(xo,yo)(y-yo)
Notice that, z = L(x,y) which represent the tangent plane approximation.

f(x,y) is called the linear approximation and is nearly equal to L(x,y),
hence the two can be used interchangeably.

We shall solve some more examples on this.



Playlists on various Course
1. Applied Electricity
   • APPLIED ELECTRICITY  

2. Linear Algebra / Math 151
   • LINEAR ALGEBRA  

3. Basic Mechanics
   • BASIC MECHANICS / STATICS  

4. Calculus with Analysis / Calculus 1 / Math 152
   • CALCULUS WITH ANALYSIS / CALCULUS 1 /...  

5. Differential Equations / Math 251
   • DIFFERENTIAL EQUATIONS  

6. Electric Circuit Theory / Circuit Design
   • ELECTRIC CIRCUIT THEORY / CIRCUIT DESIGN  

7. Calculus with Several Variables
   • CALCULUS WITH SEVERAL VARIABLES / MAT...  

Make sure to watch till the end.
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