Continuity Notes 9.19.16 Flashcards
(107 cards)
What is the basic definition of continuity?
You should be able to draw the graph of the function without lifting your pencil.
What is the actual definition of continuity?
A function is continuous if it is continuous at every point IN ITS DOMAIN
What are the three benchmarks for deciding if there is continuity at a point?
- The limit of the function approaching that point must exist
- The function must exist once the point is plugged back in
- The limit of the function approaching that point MUST EQUAL the function once the point is plugged back in
What is another word for a HOLE?
Removable Discontinuity
What are the four indicators of discontinuity at a point?
- Hole
- Jump
- Vertical Asym.
4 Oscilatting
What are three examples where the limit does not exist?
- Jump
- Vert. Asym.
- Oscillating
Do HOLES have limits?
Yes
What is the intermediate value theorem state?
If a function is on a closed interval [a,b] then you can make another function by drawing any horizontal line in between those two point starting on the y axis, and trace it till it hits the graph, using wherever it hits as the points.
What’s another way to say the Intermediate Value Theorem?
Existence Theorem
Actuar
To act
Adivinar
To guess
Alquilar
To rent
Andar
To walk, go
Apagar
To turn off the light
Arreglar
To fix
Ayudar
To help
Bailar
To dance
Bajar
To get off a bus
To go down
Cambiar
To change
Caminar
To walk
Cantar
To sing
Cenar
To have dinner
Cocinar
To cook
Comprar
To buy
