Estas son las transparencias de mi curso de Cálculo diferencial en el pizarrón electrónico correspondientes a la semana 7.

1. Continuity.
http://www.calculus-help.com/continuity/

2. Continuous functions can be
drawn with a single unbroken
pencil stroke.

3. Continuous functions can be
drawn with a single unbroken
pencil stroke.

4. Is the function shown continuous?

5. Is the function shown continuous?

6. Is the function shown continuous?

7. Is the function shown continuous?

8. Is the function shown continuous?

9. Examples.
Use the definition of continuity to determine whether or not the function
2
f(x) = 3x + x - 4 is continuous for x = 2.

10. Examples.
Sketch the graph of the function below and give the location of any
discontinuities.

11. Opener.
1. Can we use f(c) to evaluate if we know that f is a continuous
function?
2. Name one type of function for which always.
3. For what values of c can we use f(c) to evaluate if
is a rational function?

12. Removable discontinuity.
If a function f(x) is discontinuous at x = c, but exists.
Essential discontinuity.
If a function f(x) is discontinuous at x = c and does not exist.

13. Examples.
Give the location of any discontinuity.