Exploring One-Sided Limits in Calculus

The video tutorial by 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. It includes examples using an absolute value function and a piecewise function, demonstrating how to determine limits graphically using a calculator. The tutorial emphasizes understanding the notation and graphical representation of one-sided limits.

What does a negative exponent next to a constant signify in the context of one-sided limits?

• Approaching the constant from the right side

• Approaching the constant from the left side

• The function is undefined at the constant

• The limit does not exist at the constant

What symbol is used to indicate approaching from the right side in one-sided limits?

• No symbol is used

• An equal sign

• A plus sign

• A minus sign

In the context of one-sided limits, what does approaching a constant from the left side imply?

• The function's limit is positive

• The function's limit is negative

• x values are increasing away from the constant

• x values are decreasing towards the constant

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

• -2

• 0

• 2

• Undefined

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

• 2

• -2

• 0

• Undefined

For the function f(x) = |2x/x|, what is the behavior of the y-value as x approaches 0 from the left?

• It approaches -2

• It approaches 0

• It approaches 2

• It becomes undefined

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

• Only input x values greater than 1

• Use the less than symbol in the domain

• Use the greater than symbol in the domain

• Input the function without specifying the domain

What does the limit of a piecewise function as x approaches 1 from both sides indicate?

• The limit approaches a specific value from both sides

• The limit does not exist at x=1

• The function is undefined at x=1

• The function has a discontinuity at x=1

How is the domain specified for a function in a calculator for x values greater than 1?

• By inputting x values less than 1

• By using the less than symbol

• By not specifying the domain

• By using the greater than symbol

What is the limit of the piecewise function as x approaches 1 from the right side?

• 1

• -3

• 3

• 0