## Calculation of a Limit

# Limits theory

Finite Limit:

It is said that the function f(x) has for limit L when “x” moves closer to “a”, and is represented by

Infinite limit:

**PROPERTIES OF LIMITS:**

**THEOREMS:**

– 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.

**INDETERMINATE FORMS**

Subtraction

Solution: We have to multiply and divide by its conjugate.

Multiplication

Solution: We do the operation.

Division

Solution:

- 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.

Powers

Solution: We apply the following formula:

**L’Hôpital’s rule**

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 ∞ / ∞.

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