Calculate limit Using Limit Laws

In summary, limit laws are a set of rules that are used to calculate the limit of a function. These laws simplify the process of finding the limit by applying the properties of limits. To use limit laws, you must identify which law(s) apply to the given function and ensure that the limit exists. The most commonly used limit laws include the sum, difference, product, and quotient laws, which state that the limit of a sum, difference, product, or quotient of two functions is equal to the sum, difference, product, or quotient of the limits of the individual functions, respectively. However, limit laws can only be applied to continuous functions and cannot be used for indeterminate forms. In these cases, other methods, such as L
  • #1
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Homework Statement



Calculate limit Using Limit Laws

Homework Equations



Lim x+2/X^3+8 as X-->(-2)

The Attempt at a Solution




Ok so, I'm a little stumped as to what trick I need to pull out of the bag for this one. Obviously the function goes to 0/0, but I can't seem to factor anything out of the denominator to make it work. But I do know that x to the third and 8 have a cubed root. Any hints or suggestions as to what to do?
 
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  • #2
What are the limit laws.

Factor x^3 + 8 = ?
And simplify
 

Related to Calculate limit Using Limit Laws

1. What are limit laws?

Limit laws are a set of rules that can be used to calculate the limit of a function. These laws are based on the properties of limits and can help simplify the process of finding the limit of a more complex function.

2. How do I use limit laws to calculate a limit?

To use limit laws, you must first identify which law or laws apply to the given function. Then, you can apply the law(s) to simplify the function and evaluate the limit. It is important to note that limit laws can only be used when the limit exists.

3. What are the most commonly used limit laws?

The most commonly used limit laws include the sum, difference, product, and quotient laws. These laws state that the limit of a sum, difference, product, or quotient of two functions is equal to the sum, difference, product, or quotient of the limits of the individual functions, respectively.

4. Can limit laws be used for all types of functions?

No, limit laws can only be used for continuous functions. This means that the function must be defined and have a limit at the given point. If a function is discontinuous or has a limit that does not exist, limit laws cannot be applied.

5. Are there any limitations to using limit laws?

Yes, there are some limitations to using limit laws. For example, limit laws cannot be used for indeterminate forms, such as 0/0 or ∞/∞. In these cases, other methods, such as L'Hospital's rule, must be used to evaluate the limit.

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