Evaluating Limits and Expressions

The video tutorial explains how to find limits in calculus when direct substitution results in an indeterminate form like 0/0. It demonstrates two examples: one involving factoring a quadratic expression and another using the difference of cubes. The first example shows how to factor the numerator to cancel terms and find the limit. The second example involves factoring the difference of cubes to simplify the expression and determine the limit. The video emphasizes the importance of recognizing when substitution leads to indeterminate forms and using algebraic techniques to resolve them.

What is the result when you directly substitute -3 into the expression -3^2 + -3 - 6 over -3 + 3?

• 0/0

• 1/1

• 1/0

• 0/1

What does the indeterminate form 0/0 suggest about the limit?

• The limit is infinite

• Further simplification is needed

• The limit is zero

• The limit does not exist

How can the expression x^2 + x - 6 be factored?

• (x + 3)(x - 2)

• (x - 3)(x + 2)

• (x + 2)(x - 1)

• (x - 2)(x - 3)

After canceling the common terms, what expression is left to evaluate the limit as x approaches -3?

• x + 3

• x - 3

• x - 2

• x + 2

What is the final limit of the expression as x approaches -3?

• 0

• -3

• -5

• 5

What happens to the terms x + 3 in the first example after factoring?

• They are multiplied

• They are added

• They are canceled

• They are subtracted

What is the significance of the expression x - 2 in the first example?

• It is the final limit

• It is the original expression

• It is the factor that cancels

• It is the indeterminate form

What is the initial result when substituting 2 into the expression x^3 - 8 over x - 2?

• 0/0

• 1/0

• 0/1

• 1/1

What type of expression is x^3 - 8?

• Difference of cubes

• Sum of cubes

• Linear

• Quadratic

How can the expression x^3 - 8 be factored?

• (x + 2)(x^2 - 2x + 4)

• (x - 2)(x^2 + 2x + 4)

• (x - 2)(x^2 - 2x - 4)

• (x + 2)(x^2 + 2x - 4)