How would you find the limit of (an + bn) when an=-2 and bn=-16? Or just how to find limits in general?
To find the limit of a function, you can start by plugging in values that approach the desired limit. Let's use your example to explain the process.
You want to find the limit of (an + bn) as an approaches -2 and bn approaches -16.
First, simplify the expression: (an + bn) = (-2 - 16) = -18.
In this case, there is no need to go through the process of finding a limit since the expression is already a constant (-18). The limit is simply -18.
In general, to find the limit of a function, follow these steps:
1. Simplify the expression as much as possible.
2. Plug in the desired limit values for the variables.
3. If the expression simplifies to a constant, that constant is the limit.
4. If the expression is in an indeterminate form (such as 0/0 or ∞/∞), apply techniques like factoring, algebraic manipulation, or L'Hôpital's Rule to simplify the expression further.
5. If after applying the above techniques the expression still remains indeterminate, you may need to use more advanced methods like series expansion or calculus techniques.
Remember, finding limits can be more involved depending on the complexity of the expression, but these steps provide a general approach.