Calculation of a Limit
It is said that the function f(x) has for limit L when “x” moves closer to “a”, and is represented by
PROPERTIES OF LIMITS:
– The limit exists if and only if the lateral limits exist (for the right and for the left side) and both coincide.
– If there is a limit, it is unique.
Solution: We have to multiply and divide by its conjugate.
Solution: We do the operation.
- In the first case we have three possibilities:
- Numerator degree > denominator degree. The solution is ± ∞. Example:
- Numerator degree = denominator degree. The solution is the ratio of the coefficients of the same degree. Example:
- Numerator degree < denominator degree. The solution is 0. Example:
- In the second case we have to simplify common factor. In case of being rational roots, we have to multiply and divide by the conjugate of the root.
Solution: We apply the following formula:
It is a way that uses derivatives to help evaluate limits involving indeterminate forms. This rule is used when we have an uncertainty of type 0/0 or ∞ / ∞.
You can download the App BioProfe READER to practice this theory with self-corrected exercises.