Limits and Partial Derivatives of Functions of Two Variables

Tutoring on Limits and Partial Derivatives of Functions of Two Variables

Learning Objectives:

Understand and Apply Limits and Partial Derivatives of Functions of Two Variables.

Math Tutoring on Limits and Partial Derivatives of Functions of Two Variables

Limits of a Function of Two Variables:

As  approaches  the limit of  is L, if the limit from all paths approaching  exist and are equal to L.

If the function is continuous then,

First Order Partial Derivative:

The First Partial Derivative of a function of two variable tells us the slope of the tangent line at a given point in either the x or y direction. The First Partial Derivative of f with respect to x is defined by

In math tutoring, to determine , consider y as a constant and differentiate with respect to x.

The First Partial Derivatives of f with respect to y is defined by

Notation for Second Order Partial Derivatives:

 

 

 

 

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Hook Questions:

1.     State the Limits of a Function of Two Variables?

2.     Define First Order and Second Order Partial Derivative?

 

 

 

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