find the lim: lim of (x^2-3x+2)/(x^2-5x+6) as x approaches 3 from the left?

Question

A) 1/3
B) +infinity
C) - infinity
D) 1
E) none of these

Please solve step by step. I do not understand how to figure out this problem.

Answer 1

First see if you can change it into another function that is easier to deal with. If you factor your numerator and denominator then cancel, you can simplify it into:
(x - 1)/(x - 3) (These two functions are the same everywhere except at the point x = 2, where the original function had a "hole" in the graph.)

You obviously can't use substitution to find the limit as it approaches 3 (from the left). If you make a table of values or graph the function using values such as 2.5, 2.9, 2.99 (that get closer and closer from the "left" of 3), you will quickly see that the values go negative without bound. So your answer is C.

Answer 2

Plug in 3 in the expression and see what you get. If the denominator is not zero, you have the answer.

If the denominator is zero, then if the numerator is not zero, the curve goes to infinity. To find out which infinity, evaluate some points to the left of 3 and see if they go more negative or more positive as you approach 3. That tells you whether it is +infinity or -infinity.

If both are zero, factor the expression and see if you can do some canceling.

Answer 3

x^2 - 3x +2 = (x-1)(x-2)
x^2 - 5x +6 = (x-2)(x-3)

Only the second equation is 0 in x = 3
Its sign is:
..........0.........0
_+___l__-___l__+___
.........2........3

This means that x^2 - 5x + 6 will be positive is x is greater than 3 and negative is x is less than 3 (but greater than 2).

So, since the numerator tends to 3^2-3x3+2 = 2, a positive number, then the limit will be infinit, but a negative one.

Ana

Answer 4

I make this on my TI-89 Titanium and the answer was UNDEF

Answer 5

i say E
i dont even get it what r u taking super advaned atult classes