Lim x to 3 (-x^2)/((x^2)- 6x + 9)

substitution i get -9/0
factoring i get same answer
would that mean the answer is infinity?
if not how could i prove that it isn't infinity

2 answers

Often if you do not trust your answer, try numbers for example
say x = 3.1
-9.61 / (9.61 - 18.6 + 9)
= - 9.61 / .01 = -961
next try x = 3.01
but you get the idea. I think your answer is correct. The result is -9/0 which is undefined or infinite.
since x^2-6x+9 = (x-3)^2 the denominator -> 0 while the numerator does not. So, you are correct that the limit is undefined.
Similar Questions
    1. answers icon 11 answers
  1. What is the integral of 1/(x√(x^2-4)) dx?So I know that I am going to have to factor out the 4 and use the arcsec trig
    1. answers icon 1 answer
  2. I'm stuck on this one:factoring polynomials from algebraic expressions (and it says you can use the substitution method):
    1. answers icon 1 answer
    1. answers icon 1 answer
more similar questions