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 |x_{1} − 8| < |x_{2} − 8|, then |f(x_{1}) − 4|≤ |f(x_{2}) − 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 x→8 f(x) = 4, then f(8) = 4.

_____________________________________________________________________________________________

2A) Explain what it means to say that

2B) In this situation is it possible 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 x→3 f(x) cannot exist if lim x→3^{−} f(x) ≠ lim x→3^{+} f(x).

Subject | Mathematics |

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

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