Solve for Variables to Find Continuity

[Hypnos_16]

Homework Statement

y = 1 - 9x^-2 / 1 - 3x^-1 if x ≠ 3
y = a if x = 3

find the value of "a" that makes the graph Continuous at x = 3

Homework Equations

n/a

The Attempt at a Solution

I'm really not sure here, i think i must've missed this class or something, cause i just can't figure this out at all. I have two others to do too and i can't get any of them.

 

[fzero]

You might want to compute

\lim_{x\rightarrow 3} \frac{1-\frac{9}{x^2}}{1-\frac{3}{x}}

and sketch the function around x=3 to see how it behaves.

 

[Hypnos_16]

Alright, i'll try that, is there also a way to solve it mathematically? Because i don't know what way he's looking for in the question.

 

[HallsofIvy]

What fzero suggests was "mathematical"! However:
The first thing I would do is multiply both numerator and denominator by x^2 to get
\frac{x^2- 9}{x^3- 3x}= \frac{(x- 3)(x+3)}{x(x-3)}
which is the same as \frac{x+ 3}{x} as long as x is not equal to 3. What is that when x= 3?

 

[fzero]

Taking the limit and interpreting it is mathematical. I suggested to sketch since it should help picture what you're doing.