Evaluating Limits and Expressions

The video tutorial explains how to evaluate limits of rational functions as they approach infinity. It involves dividing both the numerator and the denominator by the highest power of the denominator, multiplying by the reciprocal of this power, and then substituting infinity to find the limit. The example provided results in a limit of minus two.

What is the first step when dealing with a limit that approaches infinity in a rational function?

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

• Subtract infinity from the numerator

• Multiply the numerator by infinity

• Add infinity to both the numerator and denominator

What is a rational function?

• A function with only constants

• A function with no variables

• A function that is a fraction with variables in the denominator and possibly in the numerator

• A function with variables only in the numerator

Why do we divide both the numerator and the denominator by the order of the denominator?

• To make the function more complex

• To eliminate the variables

• To simplify the expression and evaluate the limit

• To increase the value of the limit

What is the order of the denominator in the given example?

• Three

• Four

• Two

• One

What is the order of the numerator in the given example?

• One

• Two

• Three

• Four

What do we multiply the numerator and denominator by to simplify the expression?

• 1 over X squared

• 1 over X

• 1 over X cubed

• 1 over X to the fourth

What is the equivalent of the square root of one over X to the sixth?

• One over X cubed

• One over X squared

• One over X

• One over X to the fourth

What is the purpose of multiplying by the square root of one over X to the sixth?

• To increase the limit

• To simplify the expression

• To make the function more complex

• To eliminate the variables

What happens to 2 over infinity when evaluating the limit?

• It becomes 2

• It becomes infinity

• It becomes zero

• It becomes negative

What does the denominator approach when infinity is plugged in?

• Zero

• One

• Minus one

• Infinity