Understanding Limits and Factoring Techniques

The video tutorial covers evaluating limits of functions as x approaches specific values. It begins with an introduction to limits and the challenges of indeterminate forms. The instructor demonstrates how to use factoring techniques, including factoring trinomials, difference of squares, and difference of cubes, to simplify expressions and evaluate limits. The tutorial emphasizes the importance of understanding various factoring methods to solve limit problems effectively.

What is the limit of the function 5x/(x^2 + 2x) as x approaches zero?

• 0

• 5/2

• Undefined

• 1

When evaluating the limit of (x^2 + 3x - 10)/(x - 2) as x approaches 2, what is the first step?

• Cancelling terms

• Factoring the numerator

• Direct substitution

• Using L'Hôpital's rule

What is the limit of (x^2 - 9)/(x - 3) as x approaches 3?

• Undefined

• 0

• 6

• 3

How do you factor x^2 - 9?

• (x - 3)(x + 3)

• (x - 9)(x + 1)

• (x - 1)(x + 9)

• (x - 3)^2

What is the limit of (x^3 - 8)/(x - 2) as x approaches 2?

• 4

• 16

• 8

• 12

Which formula is used to factor x^3 - 8?

• Difference of squares

• Sum of cubes

• Quadratic formula

• Difference of cubes

What is the limit of (4 - x)/(x^2 - 16) as x approaches 4?

• -1/8

• 1/8

• 0

• Undefined

How do you factor x^2 - 16?

• (x - 16)(x + 1)

• (x - 8)(x + 2)

• (x - 4)(x + 4)

• (x - 2)^2

What is the limit of (2x^2 - x - 3)/(x + 1) as x approaches -1?

• -5

• 0

• 1

• Undefined

What is the first step in factoring 2x^2 - x - 3?

• Find two numbers that multiply to -6 and add to -1

• Use the quadratic formula

• Complete the square

• Direct substitution