Evaluating Limits Algebraically Quiz

What is the simplest method to evaluate a limit when the function is well-behaved at the point of interest?

• Using L'Hôpital's Rule

• Direct substitution

• Factoring the expression

• Using a conjugate

When evaluating the limit as x approaches 3 for the function (3x + 1)/(x^2 - 4), why is direct substitution valid?

• Because x = 3 results in an indeterminate form

• Because x = 3 results in a zero denominator

• Because the function is undefined at x = 3

• Because the function is well-behaved around x = 3

What should you do if direct substitution results in an indeterminate form like 0/0?

• Use a calculator to approximate

• Apply L'Hôpital's Rule

• Ignore the limit

• Factor the expression to simplify

How can factoring help in evaluating limits?

• It changes the limit to a different value

• It simplifies the expression to remove indeterminate forms

• It always results in a zero denominator

• It is only useful for polynomial functions

What is the purpose of using a conjugate when dealing with square roots in limits?

• To eliminate the square root

• To change the limit to infinity

• To create a new indeterminate form

• To simplify the expression and remove indeterminate forms

When multiplying by a conjugate, what happens to the middle terms?

• They remain unchanged

• They become zero

• They double in value

• They cancel each other out

What is a common method to simplify complex fractions when evaluating limits?

• Using a calculator

• Finding a common denominator

• Applying L'Hôpital's Rule

• Ignoring the fractions

Why is it important to find a common denominator in complex fractions?

• To make the fraction larger

• To avoid using other methods

• To simplify the expression and evaluate the limit

• To change the limit to zero

Which method is NOT typically used to evaluate limits algebraically?

• Graphing the function

• Factoring

• Using a conjugate

• Direct substitution

What is the main goal when using different methods to evaluate limits algebraically?

• To change the function's behavior

• To avoid using calculus

• To simplify the expression to allow direct substitution

• To find the exact value of the function