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Solve for Variables to Find Continuity

  • Thread starter Hypnos_16
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
fzero
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You might want to compute

[tex]\lim_{x\rightarrow 3} \frac{1-\frac{9}{x^2}}{1-\frac{3}{x}}[/tex]

and sketch the function around [tex]x=3[/tex] to see how it behaves.
 
  • #3
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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.
 
  • #4
HallsofIvy
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What fzero suggests was "mathematical"! However:
The first thing I would do is multiply both numerator and denominator by [itex]x^2[/itex] to get
[tex]\frac{x^2- 9}{x^3- 3x}= \frac{(x- 3)(x+3)}{x(x-3)}[/tex]
which is the same as [itex]\frac{x+ 3}{x}[/itex] as long as x is not equal to 3. What is that when x= 3?
 
  • #5
fzero
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Taking the limit and interpreting it is mathematical. I suggested to sketch since it should help picture what you're doing.
 

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