Understanding Limits of Piecewise Functions

The video tutorial explores the concept of limits in piecewise functions, focusing on calculating one-sided and two-sided limits. It begins with an introduction to limits and piecewise functions, followed by detailed examples of calculating limits as X approaches specific values, such as 4, 2, -1, and 0. The tutorial emphasizes understanding the function's behavior from both sides of a point and highlights scenarios where limits do not exist due to differing values from each side.

What is a piecewise function?

• A function defined by a single equation

• A function defined by multiple equations over different intervals

• A function that is always continuous

• A function that has no limits

What does the '+' sign indicate in the limit notation as x approaches 4?

• Approaching from the left

• Approaching from the right

• No specific direction

• Approaching from both sides

What is the limit of f(x) as x approaches 4 from the right?

• 4

• 3

• 2

• 1

What is the limit of f(x) as x approaches 4 from the left?

• 1

• 2

• 3

• 4

What is the limit of f(x) as x approaches 2?

• 1

• 2

• 4

• 3

What happens to the denominator of f(x) as x approaches 1?

• It remains constant

• It becomes zero

• It becomes one

• It becomes infinite

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

• 0

• 12

• 1

• Undefined

What is the limit of the new piecewise function as x approaches -1 from the left?

• Undefined

• 12

• 0

• 1

Does the two-sided limit exist as x approaches -1?

• Yes, it exists

• No, it does not exist

• It is infinite

• It is zero

What is the limit of G(x) as x approaches 0 from the right?

• Undefined

• 1

• 2

• 0