lección 2 y 3 limites y continuidad

Lectures 2 and 3 Limits and Continuity of Functions of

Several Variables

Calculus II

Topic 2:

Differential Calculus in Several Variables

Calculus II Santiago de Vicente 1


Please,…remember “Muppets”

…. and Coco (Elmo) Lessons: Learning differences between: • open and closed • disc and ball • interior and exterior • bounded and unbounded • …..


Intervals, Discs and Balls


Interior and Boundary Points

Open and Closed Disks



“Coco” (“Elmo”) Definitions

Bounded and Unbounded Sets


Unbounded Sets


Limit of a Function of Several Variables


Calculating Limits



Two-Path Test

Directional Limits (Interior Points)


Directional Limits (Boundary Points)


Directional Limits. Examples


Fundamental Properties



Some Examples


Continuity

Remember one variable Functions


Discontinuity of First Kind



Some Examples


Directional Limits (1 of 2)


Directional Limits (2 of 2)


More Examples (1 of 2)


More Examples (2 of 2)


Composite Functions


More than two variables

Homework


lección 2 y 3 limites y continuidad

Documents

variables calculus

examples calculus

balls calculus

differential calculus

kind calculus

calculating limits calculus

unbounded sets calculus

variable functions calculus