Indeterminate Forms and Factoring

The video tutorial explains how to evaluate the limit of a function as X approaches negative 3. Initially, direct substitution results in an indeterminate form, prompting the need for factoring. The numerator is factored using the difference of squares, while the denominator is factored using the sum of cubes. After canceling common factors, direct substitution is applied again, yielding a final limit of negative 2/9.

What is the result of directly substituting -3 into the expression x^2 - 9 over x^3 + 27?

• Undefined

• 0

• 0/0

• 1

Which of the following is an indeterminate form?

• 0/0

• 1/1

• 0/1

• 1/0

Which algebraic identity is used to factor the expression x^2 - 9?

• Sum of cubes

• Difference of squares

• Binomial theorem

• Quadratic formula

What is the factored form of x^2 - 9?

• (x + 3)(x - 3)

• (x + 2)(x - 2)

• (x + 9)(x - 9)

• (x + 1)(x - 1)

Which formula is used to factor the expression x^3 + 27?

• Sum of cubes

• Difference of squares

• Quadratic formula

• Binomial theorem

What is the factored form of x^3 + 27?

• (x + 3)(x^2 - x + 9)

• (x + 3)(x^2 + 3x + 9)

• (x + 3)(x^2 - 3x + 9)

• (x + 3)(x^2 + x + 9)

What is the cube of 3?

• 81

• 27

• 9

• 3

What common factor can be canceled from the numerator and denominator after factoring?

• x + 3

• x^2 - 3x + 9

• x^2 + 3x + 9

• x - 3

After canceling the common factor, what is the simplified expression for the limit?

• (x - 3)/(x^2 + 3x + 9)

• (x - 3)/(x^2 - 3x + 9)

• (x + 3)/(x^2 + 3x + 9)

• (x + 3)/(x^2 - 3x + 9)

What is the result of substituting -3 into the simplified expression (x - 3)/(x^2 - 3x + 9)?

• 1/9

• -1/9

• 2/9

• -2/9