Understanding Limits at Infinity

This lesson explains how to determine limits at infinity by focusing on the highest degree terms in the numerator and denominator of rational functions. Through three examples, the video demonstrates how to simplify these limits and understand their behavior as x approaches infinity. The first example shows a limit approaching zero, the second example results in a constant value, and the third example illustrates a limit that approaches positive infinity, indicating the limit does not exist.

What is the main concept used to determine limits at infinity in this lesson?

• Using the smallest degree terms

• Using constant terms

• Using the average of all terms

• Using the highest degree terms

In the first example, what happens to the term 3x^4 as x approaches infinity?

• It cancels out with the denominator

• It approaches zero

• It overpowers other terms in the numerator

• It becomes negligible

What is the simplified form of the limit in the first example?

• 3x

• 3/x

• x^3

• x/3

In the second example, what is the highest degree term in the denominator?

• 2x^7

• 3x^2

• x^7

• 7x^3

What is the value of the limit in the second example?

• One-half

• Infinity

• One

• Zero

In the third example, what happens to the numerator as x approaches infinity?

• It decreases

• It remains constant

• It increases without bound

• It approaches zero

What is the simplified form of the limit in the third example?

• 9x^5/2

• 2x^5/9

• 9x^2/2

• 2x^2/9

What does it mean when a limit approaches infinity?

• The limit is negative

• The limit is zero

• The limit is a real number

• The limit does not exist in the real number sense

Why is infinity not considered a real number?

• Because it is not a number

• Because it is imaginary

• Because it is not finite

• Because it is too large

What is the overall conclusion about limits at infinity?

• They indicate the limit doesn't exist in the real number sense

• They are always positive

• They are always zero

• They always exist