Understanding Limits of Sequences

The video tutorial explains how to find the limit of a sequence using a theorem that relates sequences to functions. It covers both a general method and a shortcut method for determining the limit of a rational function as n approaches infinity. The general method involves dividing each term by the highest power of n, while the shortcut method uses the degrees of the numerator and denominator. The video also includes a graphical representation to illustrate how the sequence approaches its limit.

What does the theorem suggest about the relationship between the limit of a sequence and a function?

• The limit of a sequence is always infinite.

• The limit of a sequence can be found using the limit of a related function.

• The limit of a sequence is always zero.

• The limit of a sequence is unrelated to functions.

In the general method, what is the first step to find the limit at infinity of a rational function?

• Divide each term by the highest power of n.

• Multiply each term by the highest power of n.

• Subtract the highest power of n from each term.

• Add the highest power of n to each term.

What is the purpose of dividing each term by the highest power of n in the general method?

• To simplify the expression.

• To make the expression more complex.

• To eliminate the terms.

• To increase the degree of the polynomial.

What happens to the terms with n in the denominator as n approaches infinity?

• They become negative.

• They approach zero.

• They remain constant.

• They become larger.

What is the limit of the sequence given by the rational function in the video?

• 5/6

• 1/2

• 7/6

• 3/4

According to the shortcut method, what is the limit if the degrees of the numerator and denominator are equal?

• The limit is infinite.

• The limit is the ratio of the leading coefficients.

• The limit is zero.

• The limit does not exist.

What is the degree of the numerator in the rational function discussed?

• 4

• 3

• 2

• 1

What is the degree of the denominator in the rational function discussed?

• 4

• 1

• 2

• 3

What does the graph of the sequence show about its behavior?

• The sequence oscillates.

• The sequence remains constant.

• The sequence diverges.

• The sequence converges to a specific value.

What is the approximate decimal value of the limit 7/6?

• 1.33

• 1.17

• 1.50

• 1.25