Evaluating the limit at infinity when the degrees are equal numerator, denominator

The video tutorial explains the concept of function degrees and how to rewrite them in descending power. It covers the horizontal asymptote test, emphasizing the importance of the degree in the numerator and denominator. The tutorial also discusses leading coefficients and terms, and how they relate to the degree of a function. The limit as X approaches infinity is explained in relation to horizontal asymptotes, with examples provided to illustrate the rules. The video concludes with a review of the key rules for understanding horizontal asymptotes.

What is the first step in analyzing a function for horizontal asymptotes?

• Finding the roots of the function

• Calculating the derivative of the function

• Rewriting the function in descending power

• Rewriting the function in ascending power

When the degrees of the numerator and denominator are equal, what determines the horizontal asymptote?

• The product of the coefficients

• The sum of the coefficients

• The leading coefficient of the numerator over the leading coefficient of the denominator

• The difference of the coefficients

What is the horizontal asymptote if the leading coefficient of the numerator is 2 and the denominator is 3?

• Y = 1

• Y = 5

• Y = 2/3

• Y = 3/2

What happens to the limit of a function as X approaches infinity if the degrees of the numerator and denominator are equal?

• It approaches zero

• It approaches infinity

• It equals the horizontal asymptote

• It becomes undefined

Which of the following is NOT a rule for determining horizontal asymptotes?

• If the degree of the numerator is greater, there is no horizontal asymptote

• If the degree of the denominator is greater, the asymptote is Y = 0

• If the degrees are equal, the asymptote is the ratio of leading coefficients

• If the degree of the numerator is greater, the asymptote is Y = 0