Calculating Limits Algebraically: Key Methods and Techniques

This video tutorial explores algebraic methods for solving limits, emphasizing direct substitution, factoring, simplifying complex fractions, and rationalizing. It addresses indeterminate forms and special cases, including absolute value functions, and discusses limits at infinity. The tutorial provides examples and explanations to help understand these concepts.

What is the first method to try when solving limits algebraically?

• Numerical approximation

• Graphical analysis

• Using tables

• Direct substitution

What does it mean when a limit results in 0/0?

• The limit is undefined

• The limit is zero

• The limit is indeterminate

• The limit is infinite

How can you resolve an indeterminate form of 0/0?

• By using direct substitution

• By using graphical methods

• By factoring the expression

• By using numerical methods

What should you do if factoring does not work for simplifying a limit?

• Ignore the problem

• Use a different algebraic technique

• Use a graph

• Try a different limit

What is the purpose of rationalizing the numerator or denominator?

• To avoid using algebra

• To make the expression more complex

• To eliminate radicals

• To change the limit

When dealing with limits as x approaches infinity, what should you do to simplify the expression?

• Multiply by the highest power of x in the denominator

• Use direct substitution

• Use a table of values

• Graph the function

What is the result of the limit as x approaches infinity for the expression (4 + 2/x^2 - 5/x^3) / (6 - 3/x + 4/x^2)?

• 2/3

• Infinity

• 0

• 1

How do you handle the limit of an absolute value function?

• By ignoring the absolute value

• By using a graph

• By expressing it as a piecewise function

• By using direct substitution

What is the limit of the function |x-2|/(x-2) as x approaches 2 from the left?

• 1

• 0

• Infinity

• -1

What is the limit of the function |x-2|/(x-2) as x approaches 2 from the right?

• Infinity

• 1

• -1

• 0