Weekly Homework Set 12 – Continuity

Name____________________

1. Find all points of discontinuity and discuss which part(s) of the definition for continuity fail at each point. Identify each type of discontinuity and justify your answer using the limit definitions of the discontinuities.

9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1

-1 -2 -3 -4 -5 -6 -7 -8 -9

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2 3

4

5

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7 8

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2. a) Find all points of discontinuity and discuss which part(s) of the definition for continuity fail at each point. Identify each type of discontinuity and justify your answer using the limit definitions of the discontinuities. b) If the function has a removable discontinuity at a point a, discuss what value could be assigned to f(a) to make the function continuous at that point.  1 if − ∞ < x < 1 − x 2 ,  if x = 1 f ( x) = 1, 2 x − 3, if 1 < x < 3   x − 3 + 4, if x > 3 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1

-1 -2 -3 -4 -5 -6 -7 -8 -9

y

x 1

2 3

4

5

6

7 8

9