Understanding Limits at Infinity with Square Roots

The video tutorial explains how to determine limits at infinity for functions involving square roots. It emphasizes the importance of handling absolute values correctly when factoring expressions. The tutorial walks through two examples, one where x approaches positive infinity and another where x approaches negative infinity, demonstrating the calculation of limits and the resulting horizontal asymptotes. The video concludes with graphing the function to verify the calculated limits and asymptotes.

Why is it important to be careful with signs when dealing with square roots in limits?

• Because the square root of X squared is the absolute value of X.

• Because the square root of X squared is always X.

• Because square roots are always positive.

• Because square roots can be negative.

What is the first step in simplifying a function involving square roots as X approaches positive infinity?

• Divide every term by the highest power of X.

• Factor out X from both the numerator and denominator.

• Multiply every term by X.

• Add X to both the numerator and denominator.

What is the limit of the function as X approaches positive infinity?

• 1/2

• 0

• 2

• 1

What happens to the term 5 divided by X squared as X approaches infinity?

• It approaches infinity.

• It approaches 0.

• It approaches 5.

• It remains constant.

When X approaches negative infinity, what should be factored out from the square root?

• The absolute value of X

• X squared

• -X

• X

What is the limit of the function as X approaches negative infinity?

• -1/2

• 1/2

• -1

• 0

Why is it necessary to factor out -X when X approaches negative infinity?

• Because X squared is negative.

• Because the square root of X is negative.

• Because X is positive.

• Because the absolute value of X is -X when X is negative.

What does the graph of the function verify about the limits?

• The function has no horizontal asymptotes.

• The function approaches 1 as X approaches infinity.

• The function approaches 0 as X approaches infinity.

• The function has horizontal asymptotes at Y = 1/2 and Y = -1/2.

What is the horizontal asymptote of the function as X approaches positive infinity?

• Y = 1

• Y = 0

• Y = -1/2

• Y = 1/2

What is the horizontal asymptote of the function as X approaches negative infinity?

• Y = 0

• Y = -1/2

• Y = 1

• Y = 1/2