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The word “limit” is used in everyday life to describe the ultimate behavior of something, as in the “limit of one’s endurance” or the “limit of one’s patience.” In mathematics, the word “limit” has a similar but more precise meaning.
The notation x → 3 (read “x approaches 3”) means that x takes values arbitrarily close to 3 without ever reaching 3. For example, the numbers 2.9, 2.99, 2.999, 2.9999, … approach 3 (from the left), and the numbers 3.1, 3.01, 3.001, 3.0001… approach 3 (from the right).
Please note that x → 3 means that x takes values closer and closer to 3 but never equals 3.
The limit of a function may or may not exist. If the limit of a function does exist, it must be a single number.
The notation x → 3 (read “x approaches 3”) means that x takes values arbitrarily close to 3 without ever reaching 3. For example, the numbers 2.9, 2.99, 2.999, 2.9999, … approach 3 (from the left), and the numbers 3.1, 3.01, 3.001, 3.0001… approach 3 (from the right).
Please note that x → 3 means that x takes values closer and closer to 3 but never equals 3.
The limit of a function may or may not exist. If the limit of a function does exist, it must be a single number.
Limit of a Function (aka Two Sided Limit)
Finding Limits
Limits may be found from tables of values of f(x) for x near c.
Ex A: Finding a Limit by Tables (Use the table feature in your calculator. Type the function into y1 =. “Set the table” so the independent variable is set to “ask”. When you type values into your table, start at a tenth below c, then a hundredth, then a thousandth, etc. Do the same for the right side of c. Copy the table to show your work
Assignment
Part A: Complete the tables and use them to find the given limit. Round to 3 decimal places when appropriate.
Part B: Find each limit by tables. Round to 3 decimal places when appropriate.