How to evaluate the limit to infinity of a rational function

The video tutorial covers the evaluation of limits in calculus, focusing on different methods such as direct substitution and graphing. It explains how to handle undefined limits, identify holes and asymptotes, and evaluate limits at infinity. The tutorial also discusses piecewise functions and how to graph them to understand limits at points of discontinuity.

Why is it important to understand limits through graphs?

• To prevent falling asleep

• To memorize equations

• To see how limits relate to graphs

• To avoid using calculators

What is the best method to evaluate limits according to the teacher?

• Direct substitution

• Using a ruler

• Using a graphing calculator

• Guessing the value

What happens when direct substitution results in a denominator of zero?

• The limit is zero

• The function is undefined

• The limit is infinite

• The function is continuous

How can you determine if a function has a hole or an asymptote?

• By graphing the function

• By factoring the function

• By using a calculator

• By guessing

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

• It is where the function equals zero

• It marks the end of the graph

• It shows where the function is undefined

• It indicates a hole

How do you approach limits involving infinity?

• By increasing values and observing patterns

• By using direct substitution

• By guessing the limit

• By using a calculator

What is the horizontal asymptote of a rational function with equal degrees in numerator and denominator?

• Undefined

• Infinity

• Zero

• The ratio of leading coefficients

What is the first step in graphing a piecewise function?

• Graph each function individually

• Calculate the derivative

• Find the limits

• Use a calculator

How do you determine the limit of a piecewise function at a point?

• By checking the value from the left and right

• By using a calculator

• By using direct substitution

• By guessing

What does it mean if the left and right limits of a piecewise function are not equal?

• The limit does not exist

• The function is continuous

• The function is differentiable

• The limit exists