Understanding Limits of Rational Functions

The video tutorial explains how to find the limit of a rational function as x approaches infinity. It begins with a graphical analysis, then moves to an analytical approach by multiplying factors in the numerator and denominator. The tutorial demonstrates combining like terms and using the degree of the numerator and denominator to determine the limit. An alternative method is also shown, involving dividing each term by the highest power of x in the denominator. The tutorial concludes by confirming the limit is not zero, despite appearances from the graph.

What is the initial observation about the function value as x approaches infinity?

• It remains constant.

• It oscillates.

• It approaches zero.

• It approaches infinity.

Why is the factored form of the rational function not helpful in this problem?

• The factors cancel each other out.

• The function is already simplified.

• The factors are too complex.

• There are no common factors between the numerator and denominator.

What is the result of multiplying 11 by 10x in the numerator?

• 110x

• 121

• 11x

• 10x

What is the degree of the numerator in the combined expression?

• 3

• 0

• 2

• 1

How is the limit determined when the degrees of the numerator and denominator are equal?

• By subtracting the coefficients.

• By dividing the leading coefficients.

• By adding the coefficients.

• By multiplying the coefficients.

What is the alternative method for finding the limit?

• Subtracting x from each term.

• Multiplying each term by x.

• Dividing each term by the highest power of x in the denominator.

• Dividing each term by the highest power of x in the numerator.

What happens to the terms 99/x and 121/x^2 as x approaches infinity?

• They approach zero.

• They remain constant.

• They approach infinity.

• They oscillate.

What is the final limit of the rational function as x approaches infinity?

• 10/33

• 1

• 0

• Infinity

Why might the graph initially suggest the limit is zero?

• The function value oscillates.

• The function value appears to level off.

• The function value increases rapidly.

• The function value decreases rapidly.

What is the significance of the leading coefficients in determining the limit?

• They determine the initial value.

• They determine the final limit.

• They determine the oscillation.

• They determine the rate of change.