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Continuity of Functions

Continuity of Functions

Continuity on Closed and Half-Closed Intervals Exercises

Example 1

What must be true for a function to be continuous on an interval of the form (a, b]?

Example 2

What must be true for a function to be continuous on an interval of the form [a, b]?

Example 3

Determine if f is continuous on each of the following intervals.

  • [a, b]
  • [a, b)
  • (a, b]
  • (a, b)

Example 4

Determine if f is continuous on each of the following intervals.

  • [a, b
  • [a, b
  • (a, b]
  • (a, b)

Example 5

Determine if f is continuous on each of the following intervals.

  • [a, b]
  • [a, b)
  • (a, b]
  • (a, b)

Example 6

Determine if the function 

is continuous on each of the following intervals.

  • [-1, 0]
  •  [-1, 0)
  • (-1, 0]
  • (-1, 0)
  • [0, 1]
  • [0, 1)
  • (0, 1]
  • (0, 1)

Example 7

Determine if the function 

is continuous on each of the following intervals.

  • [0, 1]
  • [0, 1)
  • (0, 1]
  • (0, 1)
  • [1, 5]
  • [1, 5)
  • (1, 5] 
  • (1, 5)