Calculus Book: pp 70-79

Question 1

continuous

Answer 1

• function continuous at x=c means that there is no interruption in the graph of f at c
• continuity can be destroyed:
• function is not defined at x=c
• the limit of f(x) does not exist at x=c
• the limit of f(x) exists at x=c, but it is not equal to f(c)

Question 2

continuity on an open interval

Answer 2

• A function is said to be continuous on an open interval if and only if it is continuous at every point in this interval

Question 3

one-sided limit

Answer 3

• either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above.

Question 4

continuity on a closed interval

Answer 4

• A function f(x) is continuous at the closed interval [a, b] if: f(x) is continuous at x for all values of x belonging to the open interval (a, b).