Limits (Algebraically and Graphically)

Which of the following is NOT a reason for a limit not existing?

• f(x) approaches a different value from the right side of c than it approaches from the left side of c

• f(x) increases or decreases without bound as x approaches c

• f(x) has a removable discontinuity at x=c (a hole)

• f(x) oscillates between two fixed values as x approaches c

• 0

• 2

• 3

• undefined

• 0

• 2

• 3

• 4

• 0

• 3

• 4

• DNE

• 0

• 3

• 4

• undefined

• 0

• 1

• 2

• DNE

• 0

• $\infty$

• $-\infty$

• DNE

• 0

• $\infty$

• $-\infty$

• undefined

• 0/0

• 1/2

• 1/4

• -1/4

• 0/0

• DNE

• -1/4

• 1/4