Understanding Limits with Absolute Values

The video tutorial explains how to evaluate limits involving absolute values by using direct substitution, left and right side limits, and piecewise functions. It covers various examples, including limits as X approaches specific values from different sides, and demonstrates how to handle cases where limits do not exist. The tutorial emphasizes the importance of checking both sides of a limit and using piecewise functions to simplify absolute value expressions.

What is the limit as X approaches 3 of the absolute value of x minus 3?

• Undefined

• 1

• 0

• 3

Why can't direct substitution be used for the limit as X approaches Z of the absolute value of x / X?

• It results in a division by zero

• It results in a negative number

• It results in a positive number

• It results in a complex number

What is the left side limit as X approaches zero of the absolute value of x/x?

• 1

• -1

• 0

• Undefined

How can the absolute value of x be expressed in terms of a piecewise function?

• x when X is positive, -x when X is negative

• x when X is zero, -x when X is non-zero

• x when X is non-zero, -x when X is zero

• x when X is negative, -x when X is positive

What is the right side limit as X approaches 5 of the absolute value of x - 5 / x - 5?

• 0

• -1

• Undefined

• 1

What is the limit as X approaches 4 from the left of the absolute value of x x - 4 over x - 4?

• 1

• -1

• 0

• Undefined

What is the limit as X approaches -2 from the left of the absolute value of x + 2 / X+ 2?

• 1

• -1

• 0

• Undefined

What is the limit as X approaches 3 from the right of the absolute value of 3 - x / x - 3?

• 0

• 1

• -1

• Undefined

How can the expression x^2 - 1 / the absolute value of x - 1 be simplified when X approaches 1 from the right?

• x + 1

• x - 1

• 1

• -1

What is the limit as X approaches 1 from the left of x^2 - 1 / the absolute value of x - 1?

• -1

• 2

• 1

• -2