No, you did NOT factor the numerator. That is not what "factor" means.l46kok said:Homework Statement
Find the limit of
[itex]\frac{x^3-2x^2-9}{x^2-2x-3}[/itex]
as x->3
Homework Equations
The Attempt at a Solution
You factor the bottom portion and top portion, then it looks something like this
[itex]\frac{x(x^2-2x)-9}{(x-3)(x+1)}[/itex]
I feel like I can go further about eliminating the demonimator but I don't know what
A limit in calculus is a fundamental concept that describes the behavior of a function as its input approaches a specific value. It is denoted by the notation "lim" and is used to determine the value that a function approaches as its input gets closer and closer to a certain value.
To find the limit of a function, you can use several methods such as direct substitution, factoring, and algebraic manipulation. You can also use the limit laws, which state that the limit of a sum, difference, product, or quotient of two functions is equal to the sum, difference, product, or quotient of their individual limits.
The notation "x->3" indicates that the value of x is approaching the number 3. In this context, it means that we are determining the limit of the function as x gets closer and closer to 3.
Finding the limit of a function is necessary because it helps us understand the behavior of the function at a specific point. It also allows us to determine if the function is continuous at that point, which is essential in many applications of calculus.
Yes, the limit of a function can be undefined. This can happen if the function has a vertical asymptote or if the left- and right-hand limits approach different values at a particular point. In the given expression, if the denominator becomes 0 as x approaches 3, the limit will be undefined.