Understanding Limits Numerically

The video tutorial explains how to determine a numerical limit by creating a table of values that approach -3 from both sides. It demonstrates how to select these values and input them into a graphing calculator to find the function values. The tutorial concludes by analyzing the graph to confirm that the limit is -6.

What is the purpose of determining a limit numerically?

• To graph a function accurately

• To solve algebraic equations

• To estimate the behavior of a function near a point

• To find the exact value of a function

How are values chosen to approach -3 from the left on a number line?

• By selecting values greater than -3

• By selecting values less than -3

• By selecting values randomly

• By selecting values equal to -3

What is the first step in using a graphing calculator to evaluate the function?

• Setting the table to 'Auto' mode

• Typing in the function

• Clearing previous calculations

• Pressing the 'Graph' button

What is the role of the 'ASK' mode in the graphing calculator?

• To graph the function

• To allow manual input of values

• To automatically generate values

• To clear previous entries

Why do we get an error when typing -3 into the function on the calculator?

• The function has a minimum at -3

• The function has a maximum at -3

• The calculator cannot process negative numbers

• The function is undefined at -3

What does the completed table indicate about the limit as values approach -3?

• The limit is equal to 0

• The limit is equal to -6

• The limit is undefined

• The limit is equal to 3

What happens to the function values as they approach -3 from the right?

• They approach 0

• They remain constant

• They approach -6

• They approach infinity

What does the graph show about the function at x = -3?

• There is a peak at x = -3

• The function is decreasing at x = -3

• There is a hole at x = -3

• The function is continuous at x = -3

What is the significance of the hole in the graph at x = -3?

• It indicates a local maximum

• It shows the function is undefined at that point

• It indicates a local minimum

• It represents a point of inflection

How does the graph confirm the limit value?

• By showing a continuous line

• By displaying a hole at the limit value

• By having a peak at the limit value

• By having a trough at the limit value