Understanding Limits at Infinity with Natural Log Functions

The video tutorial explains how to determine limits at infinity for a natural log function. It covers the analysis of limits as x approaches both negative and positive infinity, showing that both limits result in positive infinity. The tutorial uses analytical methods and verifies results with graphs and tables, emphasizing that limits approaching infinity indicate non-existence of a specific real number limit.

What is the main function discussed in the video for determining limits at infinity?

• f(x) = ln(x + 3)

• f(x) = ln(3x^2 - 2)

• f(x) = ln(2x^2 - 3)

• f(x) = ln(x^2 + 2)

As x approaches negative infinity, what happens to the input of the natural log function?

• It decreases without bound

• It remains constant

• It increases without bound

• It approaches zero

Why does the minus three in the function 2x^2 - 3 become insignificant as x approaches negative infinity?

• Because it is subtracted from a large value

• Because it is added to a large value

• Because it is multiplied by x

• Because it is a small constant

What is the limit of the function as x approaches negative infinity?

• Positive infinity

• Negative infinity

• Zero

• A specific real number

As x approaches positive infinity, what happens to the input of the natural log function?

• It increases without bound

• It decreases without bound

• It approaches zero

• It remains constant

What is the limit of the function as x approaches positive infinity?

• Negative infinity

• A specific real number

• Positive infinity

• Zero

How is the behavior of the function verified in the video?

• Using a graph and a table of values

• Using a calculator

• Using a different function

• Using a theoretical proof

What does the graph show about the function values as x approaches negative infinity?

• They increase without bound

• They oscillate

• They remain constant

• They decrease without bound

What does the graph show about the function values as x approaches positive infinity?

• They decrease without bound

• They remain constant

• They increase without bound

• They oscillate

What is the overall conclusion about the limits of the function as x approaches both negative and positive infinity?

• The limits are specific real numbers

• The limits are positive infinity

• The limits are negative infinity

• The limits are zero