Question

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.

Answer 1

For
`x\\eq a`, we have


`(x^2-a^2)/(x-a)=((x-a)(x+a))/(x-a)=x+a`

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


`\displaystyle\lim_(x\to a)g(x)=\lim_(x\to a)(x+a)=2a=4\implies a=2`