Limits and Boundaries

Limits and Boundaries

The Concept of Limit:

• When a sequence, function, or series approaches a specific value, it is known as approaching a limit.
• A function F(x) approaches a limit L as x approaches a certain value c, often denoted as the limit of F(x) as x approaches c equals L.
• The limit of a function can be from both the left (limit as x approaches c^-) and right (limit as x approaches c^+).
• Limits can be finite or infinite and do not have to exist.

Working with Limits:

• Limit laws simplify the process of finding limits.
• Algebraic methods including direct substitution, factoring and cancellation, may be used to solve limits.
• If no algebraic method works, you could try using one-sided limits or hopital’s rule.

Boundaries:

• Boundaries often appear in conversation about inequalities.
• The values which an inequality does not surpass constitute its limits or boundaries.
• A boundary could be inclusive (a closed set) or non-inclusive (an open set).

Working with Boundaries:

• To solve an inequality and find its boundaries, treat it similar to an equation, maintaining the inequality direction.
• Always consider whether the given number is inside or outside the boundary. Swap the inequality if you multiply or divide by a negative number.
• Display the answer as an inequality, in set notation or on a number line.