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Calculus I (Practice Problems) / Limits / Continuity   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Practice Problems
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Limits At Infinity, Part II Previous Section   Next Section The Definition of the Limit

1.  The graph of  is given below.  Based on this graph determine where the function is discontinuous.

[Solution]

 

2. The graph of  is given below.  Based on this graph determine where the function is discontinuous.

[Solution]

 

For problems 3  7 using only Properties 1  9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the given function is continuous or discontinuous at the indicated points.

 

3.  

   (a)  , (b) , (c) ? [Solution]

 

4.  

   (a)  (b) (c) ? [Solution]

 

5.  

    (a)  , (b) ? [Solution]

 

6.  

    (a)  , (b) ? [Solution]

 

7.  

    (a)  , (b) ? [Solution]

 

For problems 8  12 determine where the given function is discontinuous.

 

8.  [Solution]

 

9.  [Solution]

 

10.  [Solution]

 

11.  [Solution]

 

12.  [Solution]

 

For problems 13  15 use the Intermediate Value Theorem to show that the given equation has at least one solution in the indicated interval.    Note that you are NOT asked to find the solution only show that at least one must exist in the indicated interval.

13.  on  [Solution]

 

14.  on  [Solution]

 

15.  on  [Solution]

 

Problem Pane
Limits At Infinity, Part II Previous Section   Next Section The Definition of the Limit
Review Previous Chapter   Next Chapter Derivatives

Calculus I (Practice Problems) / Limits / Continuity    [Notes] [Practice Problems] [Assignment Problems]

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