Find the Limits of f(x)=(x^2-16)/(sqrt(x^2-8x+16)) at x=4

[chukie]

Hi I was wondering if someone could help me with this limit problem:

Find the lim x->a-, lim x->a+ and lim x->a
for the f(x)=(x^2-16)/(squareroot(x^2-8x+16)) a=4

I've tried to simplify the problem but after that i don't know wut to do =(
This is wut I've done:
y=(x^2-16)/(squareroot(x-4)^2)
y=(x^2-16)/abs(x-4)

any help would be appreciated.

 

[Modern Algebr]

y=(x^2-16)/abs(x-4)
= x+4,x>4
=-x-4,x<4
this is a piece wise function, mow you can easily find the left,right limit
Note:Limit of f(x) as x approaches 4 doesn't exist as left and right limit at x=4 are not equal

The more intuitive way is to draw the graph of the piecewise function!