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Question part points submissions used consider the following. g(x)={((x**2-a**2)/(x-a) text(if ) x != a,4 text(if ) x =
a.find the constant a such that the function is continuous on the entire real line.

Respuesta :

LammettHash
For [tex]x\neq a[/tex], we have

[tex]\dfrac{x^2-a^2}{x-a}=\dfrac{(x-a)(x+a)}{x-a}=x+a[/tex]

So for [tex]g(x)[/tex] to be continuous at [tex]x=a[/tex], we require that the limit as [tex]x\to a[/tex] is equal to 4.

[tex]\displaystyle\lim_{x\to a}g(x)=\lim_{x\to a}(x+a)=2a=4\implies a=2[/tex]

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