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 May 8th, 2013, 11:25 AM #1 Newbie   Joined: May 2013 Posts: 3 Thanks: 0 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
 May 8th, 2013, 11:31 AM #2 Newbie   Joined: May 2013 Posts: 3 Thanks: 0 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.
 May 8th, 2013, 12:37 PM #3 Senior Member   Joined: Feb 2012 Posts: 628 Thanks: 1 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 $\frac{f(b) - f(a)}{b - a}$, which is 0 if $f(b)= f(a)$, but this alone does not guarantee that $f(c)= f(a)$ for every point c between a and b.
May 8th, 2013, 12:55 PM   #4
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Re: limit statements true or not?

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 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 $\frac{f(b) - f(a)}{b - a}$, which is 0 if $f(b)= f(a)$, but this alone does not guarantee that $f(c)= f(a)$ 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

 May 10th, 2013, 08:35 AM #5 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 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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