Understanding Limits at Infinity

The video tutorial covers the concept of limits at infinity, explaining their significance in understanding the end behavior of functions. It introduces a theorem for determining limits at infinity and demonstrates how to analyze these limits using graphs and tables. The tutorial also discusses horizontal asymptotes and provides practical examples and shortcuts for finding limits at infinity in rational functions.

What is the primary goal of studying limits at infinity?

• To determine the behavior of a function as inputs grow larger

• To find the maximum value of a function

• To find the roots of a polynomial

• To calculate the derivative of a function

According to the theorem discussed, what happens to the limit of C divided by X to the power of R as X approaches infinity?

• It approaches zero

• It remains constant

• It approaches infinity

• It becomes undefined

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CCSS.HSF-IF.C.7D

What is a horizontal asymptote in the context of limits at infinity?

• A line that the graph of a function approaches as X approaches infinity

• A point where the graph of a function crosses the X-axis

• A vertical line that the graph of a function approaches

• A line that the graph of a function never touches

When the degree of the numerator is less than the degree of the denominator in a rational function, what is the limit as X approaches infinity?

• The limit is infinity

• The limit is zero

• The limit is the ratio of the leading coefficients

• The limit does not exist

In the example of the function 1 divided by X + 3, what is the limit as X approaches infinity?

• 1

• Infinity

• 0

• 3

What is the result of dividing each term by the highest power of X in the denominator when finding limits at infinity?

• It eliminates the need for a graph

• It changes the degree of the function

• It makes the function more complex

• It simplifies the function to find the limit

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CCSS.HSF-IF.C.8B

In the example of 2X + 5 divided by X - 1, what is the limit as X approaches negative infinity?

• Negative infinity

• Infinity

• 2

• 0

What does it mean if the degree of the numerator is greater than the degree of the denominator in a rational function?

• The limit is zero

• The limit is the ratio of the leading coefficients

• The limit does not exist

• The limit is negative infinity

In the final example, what is the limit of the function as X approaches infinity?

• Negative infinity

• 2

• Infinity

• 0

What technique is used to verify the limit of a function graphically?

• Factoring the function

• Finding the roots

• Calculating derivatives

• Using a T-table