limits and continuity of functions of two or ......limits and continuity of functions of two or more...

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LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A.

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Page 1: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

LIMITS AND CONTINUITY OF FUNCTIONS OF TWOOR MORE VARIABLES.

Examples Solved

Universidad Autónoma de Occidente

Victor H. Gil A.

Page 2: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Finding Limits Using the Numerical

Method

Page 3: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 1.

Page 4: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A
Page 5: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 2.

Page 6: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 3.

Page 7: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Finding Limits Using the

Analytical Method

Page 8: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 4.

Example 5.

STOP

Page 9: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 7.

Example 6.

Page 10: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Limits Along a Path

Page 11: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 8.

Page 12: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A
Page 13: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 9.

Page 14: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A
Page 15: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 10.

Page 16: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 11.

Page 17: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Changeof

Coordinates

Page 18: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 11.

Page 19: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Theoremor

Sandwich

Page 20: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 12.

Page 21: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A
Page 22: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Continiuty

Page 23: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

STOP

Page 24: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 13.

Example 14.

Example 15.

Example 16.

Page 25: LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR ......LIMITS AND CONTINUITY OF FUNCTIONS OF TWO OR MORE VARIABLES. Examples Solved Universidad Autónoma de Occidente Victor H. Gil A

Example 17.