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May 8th, 2013, 11:25 AM   #1
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limit statements true or not?

which of the following statements MUST be true, MIGHT be true, or is NEVER true about a function f which is defined for all real numbers? Justify your answer.


a) lim x->a f(x)=f(a) might be true if this is a continuous function

b)If lim x-> f(x)/x=1 then lim x->0 f(x)=0
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May 8th, 2013, 11:31 AM   #2
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Re: limit statements true or not?

and also c) If the average rate of change of a function between two points is zero, then the function is constant between those two points.
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May 8th, 2013, 12:37 PM   #3
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Re: limit statements true or not?

Statement A must be true, because if it was not true, then there would be a discontinuity at x = a.

Statement B is unclear. (The limit as x approaches what value of f(x)/x?)

Statement C might be true, although it probably isn't. The average rate of change on an interval (a, b) is just , which is 0 if , but this alone does not guarantee that for every point c between a and b.
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May 8th, 2013, 12:55 PM   #4
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Re: limit statements true or not?

Quote:
Originally Posted by icemanfan
Statement A must be true, because if it was not true, then there would be a discontinuity at x = a.

Statement B is unclear. (The limit as x approaches what value of f(x)/x?)

Statement C might be true, although it probably isn't. The average rate of change on an interval (a, b) is just , which is 0 if , but this alone does not guarantee that for every point c between a and b.
oh i meant for statement b: b)If lim x->0 f(x)/x=1 then lim x->0 f(x)=0
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May 10th, 2013, 08:35 AM   #5
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Re: limit statements true or not?

If the numerator of a fraction goes to 0 and the denominator does not what happens to the fraction?
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