Evaluating Limits and Asymptotes

The video tutorial explains how to evaluate limits at infinity, focusing on rational functions. It demonstrates dividing the numerator and denominator by the highest power of X in the denominator. Two examples are provided: one for limits as X approaches infinity and another for negative infinity. The tutorial also covers non-rational functions using conjugates and analyzes graphs to identify infinite limits and asymptotes.

What is the main strategy for evaluating limits at infinity for rational functions?

• Multiply the numerator and denominator by the highest power of X in the numerator.

• Divide the numerator and denominator by the highest power of X in the denominator.

• Add the highest power of X to both the numerator and denominator.

• Subtract the highest power of X from both the numerator and denominator.

In Example 1A, what happens if you try direct substitution for the limit as X approaches infinity?

• You get zero.

• You get a finite number.

• You get an infinity over infinity, which is undefined.

• You get a negative number.

What is the result of dividing all terms by the highest power of X in Example 1A?

• The terms become larger.

• The terms become smaller and approach zero.

• The terms remain unchanged.

• The terms become negative.

In Example 1B, what is the limit of 11/x^2 as X approaches negative infinity?

• Infinity

• Negative infinity

• One

• Zero

What is a horizontal asymptote?

• A line that the graph of a function never touches.

• A line that intersects the graph of a function at multiple points.

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

• A vertical line that the graph of a function approaches.

In Example 2, what method is used to evaluate limits at infinity for non-rational functions?

• Using the conjugate to create a difference of squares.

• Dividing by the highest power of X.

• Adding a constant to both the numerator and denominator.

• Subtracting a constant from both the numerator and denominator.

What happens to the terms in the numerator when using the conjugate in Example 2?

• They remain unchanged.

• They become negative.

• They cancel out.

• They become larger.

In Example 3, what indicates a vertical asymptote on a graph?

• The function crosses the x-axis.

• The function approaches a finite value.

• The function remains constant.

• The function approaches infinity or negative infinity.

What is the limit of f(x) as X approaches infinity in Example 3?

• Infinity

• 4

• 2

• Zero

What is the significance of a horizontal asymptote in a function?

• It shows the value the function approaches as X goes to infinity or negative infinity.

• It is the minimum value of the function.

• It indicates where the function crosses the x-axis.

• It is the maximum value of the function.