You have made a mistake. You should not get zero in the numerator. Check your signs.Jan Hill said:When I work this out, I get zero in the numerator. I don't know how to get the indeterminate form, [inf/inf] that you got. How do you get that?
Jan Hill said:I end up with 2x^2 - 2x^2 in the numerator when I myultiply by the conjugate.
The limit as x approaches infinity refers to the value that a function approaches as the input (x) becomes infinitely large. In other words, it is the value that the function gets closer and closer to as the input increases without bound.
Finding the limit as x approaches infinity is important because it helps us understand the behavior of a function as the input values get larger and larger. It can also help us determine if a function has an asymptote (a line that the function gets closer to but never reaches) at infinity.
To find the limit as x approaches infinity, you can use several methods such as substitution, factoring, or algebraic manipulation. Another method is to graph the function and observe the behavior as x gets larger. In some cases, you may need to use L'Hopital's rule or other advanced techniques.
Some common types of limits as x approaches infinity include polynomials, rational functions, exponential functions, and logarithmic functions. These types of limits may have different methods for finding the limit, but the concept of approaching infinity remains the same.
Yes, it is possible for a function to have a limit as x approaches infinity. For example, the limit of a polynomial or rational function as x approaches infinity will always approach either positive or negative infinity. However, there are also cases where a function does not have a limit as x approaches infinity, such as oscillating or oscillating functions.