Properties of Limits 
When computing the value of a limit, it's possible to find one of these situations:

If a limit exists, the following properties of limits give us the necessary tools to compute it. Below we assume these limits exist:
Sum / Subtraction RuleThis rule states that the limit of the sum or subtraction of two functions is equal to the sum or subtraction of their limits:
Constant Function RuleThe limit of a constant function is the constant:
Constant Multiple RuleThe limit of a constant times a function is equal to the product of the constant and the limit of the function:
Product RuleThe limit of the product of two functions is the product of their limits
Quotient RuleThe limit of quotient of two functions is the quotient of their limits, provided that the limit in the denominator function is not zero:
Power RuleThe limit of the power of a function to a given exponent n is the power n of the limit, where n is any real numberThis can be applied to the particular case of radicals:
ExampleFind the following limit:
Appliyng the quotient rule:
Appliyng the sum / subtraction rule:
The next step requires the application of the power rule (for radicals), constant Multiple rule, and the constant function rule:
Operating into the radical and substituting in the explicit functions:
Operating the rest of the limits and simplifying:
