Prove It said:I don't understand why you can't find the answer using algebra?
If you divide by a big number, your total amount is small.
If you divide by a small number, your total amount is big.
Here, the denominator is getting closer to 0 (so very small), so what do you think happens to the whole amount?
nycmathdad said:I am learning this material on my own with very limited time on my hand. Be a little more understanding in your reply. The limit is negative infinity. How is this done using a table of values?
Prove It said:Why do you need a table of values at all? You have already established that the limit is $-\infty$ because the denominator gets extremely small, and the function has negative values on both sides.
A rational function is a mathematical function that can be expressed as the ratio of two polynomial functions.
The limit of a rational function is the value that the function approaches as the independent variable approaches a certain value or approaches infinity.
To find the limit of a rational function, you can use the rules of limits such as direct substitution, factoring, and common denominator. You can also use L'Hopital's rule for more complex functions.
If the limit of a rational function does not exist, it means that the function does not approach a single value as the independent variable approaches a certain value or approaches infinity. This can happen if the function has a vertical asymptote or if the limit from the left and right sides of the value are not equal.
The limit of a rational function is important because it helps us understand the behavior of the function near a certain value or as the independent variable approaches infinity. It can also help us determine the end behavior of the function and identify any asymptotes.