Connecting Multiple Representations of Limits

Mr. Bean introduces a calculus lesson focused on connecting different representations of functions, such as piecewise functions, tables, and graphs. The lesson emphasizes understanding when limits do not exist and how to analyze them using algebraic methods. It also covers finding limits involving absolute values, a common topic in AP exams. The lesson is designed to be concise and reinforces previously learned concepts.

What is the main focus of this lesson?

• Solving complex integrals

• Reviewing algebraic equations

• Connecting different representations of functions

• Introducing new calculus concepts

In a piecewise linear function, what does it mean if the limit as X approaches 5 does not exist?

• The left and right limits are equal

• The function is continuous at X=5

• The left and right limits are not equal

• The function has a maximum at X=5

How can you determine if the limit does not exist using a graph?

• By checking if the function is increasing

• By finding the derivative at the point

• By comparing the left and right limits

• By checking if the graph is continuous

What is the result of plugging in 5 into the left side of the piecewise function 2x - 1?

• 8

• 11

• 9

• 10

Why does the piecewise function 2x - 1 and 14 - x not work for a limit that does not exist?

• Because the function is undefined at X=5

• Because the left and right limits are different

• Because the function is not linear

• Because the left and right limits are the same

When analyzing a table of values, what indicates that the limit does not exist?

• The function is continuous

• The Y-values are increasing

• The left and right Y-values are not approaching the same value

• The X-values are decreasing

What is the Y-value approaching from the left side of 5 in the given table of values?

• 8

• 4

• 1

• 6

How do you find the limit when an absolute value is involved?

• By using a calculator

• By graphing the function

• By plugging in numbers close to the target value

• By finding the derivative

What is the result of dividing the absolute value of a negative number by the same negative number?

• 1

• 0

• Negative 1

• Undefined

What should you do after completing this lesson?

• Start a new topic

• Take the mastery check

• Review the previous lesson

• Skip to the next lesson