Strategies for Determining Limits in Calculus

What is the first step in finding limits using direct substitution?

• Multiply by the conjugate

• Factor the expression

• Plug the value into the function

• Simplify the fraction

What is the result of direct substitution if the limit results in 0/0?

• The limit is undefined

• The limit is zero

• The limit is infinite

• The limit is indeterminate

What is the purpose of multiplying by the conjugate when rationalizing fractions?

• To simplify the numerator

• To factor the expression

• To cancel out terms

• To eliminate the radical

In the example problem, what is the conjugate of (√x + 4) - 3?

• (√x - 4) - 3

• (√x - 4) + 3

• (√x + 4) + 3

• (√x + 4) - 3

What is the final answer for the limit problem involving the radical on the bottom?

• -6

• 1/3

• 1/6

• 1/9

What is the first step in solving a complex fraction limit problem?

• Multiply by the conjugate

• Get common denominators

• Factor the numerator

• Simplify the fraction

What is the greatest common factor used for in complex fractions?

• To simplify the numerator

• To eliminate the denominator

• To factor the expression

• To find common denominators

What is the final answer for the complex fraction limit problem involving 4 times (x - 4)?

• 16

• 4

• -16

• -4

In the second complex fraction example, what is the result of factoring out an X from the numerator?

• -X + 6

• -X - 6

• X - 6

• X + 6

What is the final simplified answer for the second complex fraction example?

• -2/3

• -2/27

• 2/3

• 2/27