find the constant a , such that the function is continuous on the entire real number line.
g(x) = x^2 - a^2/ x-a , where the x is not equal to a
8 , where x is equal to a.

so, how can i know the contanst of a ? please help me

Question

find the constant a , such that the function is continuous on the entire real number line. 
g(x) = x^2 - a^2/ x-a , where the x is not equal to a
          8 , where x is equal to a.

so, how can i know the contanst of a ? please help me

anonymous · Answer

$a$ is not equal to $8$ ?

anonymous · Answer

no matter, here is the gimmick
factor and cancel , then replace $x$ by $a$

anonymous · Answer

$$\frac{x^2-a^2}{x-a}=\frac{(x+a)(x-a)}{x-a}=x+a$$ if $x\neq a$

anonymous · Answer

the limit as $x\to a$ will be $2a$
question is worded strangely

anonymous · Answer

ooooh i see !! it is find $a$ so that the limit is $8$! i get it

anonymous · Answer

since as we see above, the limit will be $2a$ so it $2a=8$ then $a=4$ doe, sorry i didn't understand the question

anonymous · Answer

@satellite73  thanks for the response =) 
but how u got the 2a? it's a bit confusing. hee

hartnn · Answer

$\Large \lim \limits_{x \to a}f(x) = f(a)$

basically, whenever you can, plug in x=a directly in the function.

hartnn · Answer

$\Large x+a |_{x \to a} = a+a = 2a$

anonymous · Answer

ok thanks @hartnn . i got it =)

hartnn · Answer

welcome ^_^