1.4   Continuity

EXERCISES

For problems #1-3, let  g  be the piecewise defined function given by the equations on the left and graphed on the right:

1.  Is g continuous at x=2?

2.  Where does g have step discontinuities?

3.  Where does g have removable discontinuities?

4.  Classify any points of discontinuity of f over the graphed interval.

Find any points of discontinuity of the functions in problems #5-10.   Specify whether or not the discontinuity is removable.

5.  

 6.  

7.  

8.   

9.   

10.  

For problems 11-13, what value of a makes the function continuous at x=1?

11.    

12.  

13.  

14.   Use the Intermediate Value Theorem to show that the equation   cos x = x   must have at least one solution.

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