Exploring One-Sided Limits in Calculus

In this video, Mr. Banker explains the concept of one-sided limits, focusing on how functions behave as they approach a specific x-value from either the left or right side. He uses graphical examples to demonstrate these limits, including an absolute value function and a piecewise function. The video highlights how to determine limits from both sides and the significance of these calculations in understanding function behavior.

What does approaching a specific number from the left-hand side indicate in one-sided limits?

• It is represented by a plus sign next to the constant.

• It means the function is undefined at that point.

• It is shown by a little negative sign next to the constant.

• It indicates the function's value is positive.

What symbol indicates approaching from the right-hand side in one-sided limits?

• A minus sign next to the constant.

• No specific symbol is used.

• A plus sign next to the constant.

• A division symbol next to the constant.

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CCSS.HSF.IF.A.2

What is the limit of f(x) = |2x/x| as x approaches 0 from the left-hand side?

• 0

• 2

• Undefined

• -2

What is the limit of f(x) = |2x/x| as x approaches 0 from the right-hand side?

• 0

• Undefined

• 2

• -2

How is the function f(x) = |2x/x| graphically analyzed for its limit?

• Through estimation only.

• By drawing the graph without technology.

• By plotting points manually.

• Using a calculator's graph function.

How do you graph a function for x values less than 1 on a calculator?

• Graph without specifying the domain.

• Use the greater than symbol in the domain.

• Put the function in parentheses and divide by the domain.

• Only input x values greater than 1.

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Why does the point at x=1 not exist for the piecewise defined function?

• Because it's defined for x values less than 1 only.

• Because it's defined for x values greater than 1 only.

• Both functions are not defined for an x value of 1.

• Due to a calculation error.

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CCSS.HSF-IF.C.7B

How can you graph a function for x values greater than 1 on a calculator?

• By not specifying the domain.

• Using the less than symbol in the domain.

• Putting the function in parentheses and dividing by the domain.

• Graphing without parentheses.

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

What does the limit of a piecewise defined function as x approaches 1 from the left-hand side equal?

• 4

• 2

• 3

• 1

What does the limit of a piecewise defined function as x approaches 1 from the right-hand side equal?

• 4

• 1

• 3

• 2