Understanding Limits and Limit Laws

The video tutorial explains how to evaluate limits using limit laws. It covers examples including the limit of a difference, the limit of a square root, the limit of a natural logarithm, and the limit of a quotient. Each example demonstrates the application of specific limit laws to find the exact value of the limit as x approaches a given point.

What is the purpose of using limit laws in evaluating limits?

• To approximate values of functions

• To find exact values of functions

• To avoid using calculus

• To simplify complex expressions

In Part A, what is the result of evaluating the limit of f(x) - 8 * g(x) as x approaches 8?

• 8

• -7

• 57

• 64

Which limit law is used to evaluate the limit of a difference?

• Limit of a product

• Limit of a quotient

• Limit of a sum

• Limit of a difference

In Part B, what is the limit of the square root of h(x) as x approaches 8?

• 4

• 8

• 2

• 16

What is the result of the limit of the natural log of h(x) as x approaches 8?

• Natural log of 2

• Natural log of 4

• Natural log of 16

• Natural log of 8

Which limit law is applied to evaluate the limit of a natural log?

• Limit of a difference

• Limit of a natural log

• Limit of a product

• Limit of a sum

In the final example, what is the result of the limit of f(x) / g(x) as x approaches 8 plus 1?

• 1

• 8

• 158

• 57

What is the limit of a quotient equal to?

• A product of limits

• A quotient of limits

• A sum of limits

• A difference of limits

What is the common denominator used in the final example?

• 1

• 8

• 57

• 16

What is the final simplified result of the expression in the last example?

• 57

• 158

• 8

• 1