Understanding Limits at Infinity

This video tutorial explains how to find limits at infinity for various functions. It covers polynomial functions, rational functions, and the concept of bottom-heavy and top-heavy functions. The tutorial provides examples and step-by-step solutions to help understand how to determine the limits as x approaches infinity or negative infinity.

What happens to the value of x squared as x approaches positive infinity?

• It approaches zero

• It becomes a negative number

• It approaches positive infinity

• It remains constant

When x approaches negative infinity, what is the limit of x cubed?

• One

• Zero

• Negative infinity

• Positive infinity

In a polynomial function, which terms can be ignored when finding the limit at infinity?

• All terms

• The terms with the lowest degree

• The constant terms

• The terms with the highest degree

What is the limit of 1/x as x approaches infinity?

• Zero

• Infinity

• One

• Negative infinity

For a rational function where the degree of the denominator is greater than the numerator, what is the limit as x approaches infinity?

• Zero

• Infinity

• One

• Negative infinity

How do you find the limit of a rational function where the degrees of the numerator and denominator are equal?

• Subtract the coefficients

• Multiply the coefficients

• Divide the coefficients

• Add the coefficients

What is the limit of (8x^2 - 5x) / (4x^2 + 7) as x approaches infinity?

• 1

• Infinity

• 0

• 2

In a top-heavy rational function, which terms are most significant when finding the limit at infinity?

• All terms

• The constant terms

• The terms with the highest degree in the numerator

• The terms with the lowest degree

What is the limit of (5x + 6x^2) / (3x - 8) as x approaches infinity?

• Infinity

• 2

• Zero

• Negative infinity

For a top-heavy rational function, what is the general behavior of the limit as x approaches infinity?

• It approaches zero

• It becomes a negative number

• It approaches positive infinity

• It remains constant