Project #20380 - Calculus (2 problems)

1A) Explain what is meant by the equation

lim x 8 f(x) = 4.

 1)
2) The values of f(x) can be made as close to 4 as we like by taking x sufficiently close to 8.
4) If |x1 8| < |x2 8|, then |f(x1) 4| |f(x2) 4|.


B) Is it possible for this statement to be true and yet f(8) = 7? Explain.

 1)
2) Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 7.
 
4) No, if lim xf(x) = 4, then f(8) = 4.
 
_____________________________________________________________________________________________
2A) Explain what it means to say that
lim x 3 f(x) = 6  and  lim x 3+ f(x) = 7.
 1)
2) As x approaches 3 from the left, f(x) approaches 6. As x approaches 3 from the right, f(x) approaches 7.
3)
4) As x approaches 3, f(x) approaches 7, but f(3) = 6.

2B) In this situation is it possible that
lim x 3 f(x)
exists? Explain.
 1)
2) Yes, f(x) could have a hole at (3, 7) and be defined such that f(3) = 6.
 
4) No, lim xf(x) cannot exist if lim x3 f(x)  lim x3+ f(x).
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Subject Mathematics
Due By (Pacific Time) 12/31/2013 02:00 pm
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