The results of a survey are shown below. In the survey, 12 students said that they would like to learn French. How many of the s
tudents surveyed would like to learn Spanish?
2 answers:
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For 
to be continuous at 
, you need to have the limit from either side as 
to be the same.
If
and 
, then the limit from the right would be 
, so the answer to part (1) is no, the function would not be continuous under those conditions.
This basically answers part (2). For the function to be continuous, you need to satisfy the relation
.
Part (c) is done similarly to part (1). This time, you need to limits from either side as
to match. You have
So,
and 
have to satisfy the relation 
, or 
.
Part (4) is done by solving the system of equations above for and . I'll leave that to you, as well as part (5) since that's just drawing your findings.
If
This basically answers part (2). For the function to be continuous, you need to satisfy the relation
Part (c) is done similarly to part (1). This time, you need to limits from either side as
So,
Part (4) is done by solving the system of equations above for