limits & continuity

Complete

Summary

Rules

Trigonometric functions

Standard limit of trigonometric functions

Concept

Limit exists

  • behaviour around c

function converges on the same value when approaching from both sides

Continuous

  • no breaks at c

Squeeze/sandwich theorem

  • limit of a function bounded by two other functions

squeeze_theorem.png

Intermmediate value theorem

Definition of limit

  • by making as close as possible to , we make as close to
  • for each degree of closeness to , there is a corresponding closeness to

Application

Limits of reciprocal

Limits with absolute values

Applying standard limits of trigonometric functions

Limits with trigonometric functions

Squeeze theorem and absolute

Extra

Distributes with simple arithmetic