Limits and Algebraic Techniques

The video tutorial provides a review for an upcoming quiz covering sections 1.1 through 1.3, focusing on limits. It explains limits graphically by interpreting graphs and analytically using algebraic methods such as factoring and multiplying by conjugates. The tutorial also covers special trigonometric limits and properties of limits, providing examples and solutions to enhance understanding.

What sections does the upcoming quiz cover?

• 1.4 to 1.6

• 2.1 to 2.3

• 2.4 to 2.6

• 1.1 to 1.3

Which method involves looking at a picture to understand limits?

• Graphical

• Analytical

• Numerical

• Theoretical

What is the y-value of f(0) in the given graph?

• 0

• 1

• 5

• 11

What does DNE stand for in the context of limits?

• Does Not Equal

• Does Not Exist

• Do Not Enter

• Do Not Evaluate

What is the limit as x approaches 2 in the given graph?

• 5

• 3

• 4

• 6

What algebraic method is used to solve limits when direct substitution results in 0/0?

• Factoring

• Integration

• Graphing

• Differentiation

What is the result of factoring x^2 - 16?

• (x-8)(x+8)

• (x-1)(x+1)

• (x-4)(x+4)

• (x-2)(x+2)

What technique involves multiplying by the conjugate to solve limits?

• Factoring

• Graphing

• Differentiation

• Using Conjugates

What is the conjugate of √x + 1?

• x + 1

• √x + 1

• x - 1

• √x - 1

What is the limit of 1/(√x + 1) as x approaches 0?

• 0

• 2

• 1/2

• 1