The discussion centers around finding limits of expressions, specifically polynomial and rational functions, without the aid of graphs. The original poster seeks clarification on the methods for evaluating limits, particularly at a specific point.
Some participants have provided guidance on evaluating limits for polynomials and rational expressions. There is an acknowledgment of the potential complications that arise when encountering indeterminate forms like 0/0, indicating a productive exploration of the topic.
Participants are navigating the nuances of limit evaluation, including the difference between continuous functions and those that may require factoring or further analysis when limits yield indeterminate forms.
939 said:Homework Statement
I cannot remember how to do this. How do you find the limit of expressions, without graphs of them?
Homework Equations
i.e.
lim x -> 3 (x^2 - 5x + 2)
The Attempt at a Solution
1) (3 + h)^2 - 5(3 + h) + 2
= (3 + h)(3 + h) - 15 - 5h + 2
9 + 6h - h^2 - 15 - 5h + 2
-4 - 1h - h^2
...
The book says it is -4, but is this the right method? Will it work for rational expressions too?
Mark44 said:f(x) = x2 - 5x + 2 is a polynomial, hence it is continuous everywhere. To find the limit of f as x → 3, simply evaluate f(3). You should get -4.
It looks like you are misremembering part of the difference formula in the definition of the derivative.
939 said:Thanks, got it.
In the case of a rational expression, I merely:
1) Evaluate at f(#)
2) If that = 0, try to see if it can be factored and then evaluate again
Correct?