Math CentralQuandaries & Queries


Question from norma, a student:

I have a problem like this one but I can get it right. please help me to answer
find the constant a such that the function is continuous on the entire line.
g(x)= {x^2 - a^2 / x-a if x is not = a
         {6 if x = a

Hi Norma,

As long as x is not equal to a, (x2 - a2)/(x - a) = (x - a)(x + a)/(x - a) = x + a which is continuous. Thus the only point left to consider is x = a.

For g(x) to be continuous you must have


You know that g(a) = 6 so you need


What is the value of the limit? This give you an equation which you can solve for a.


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