Why can't we use direct substitution when the denominator becomes zero?
Evaluate the limit of a rational expression by applying direct substitution
Interactive Video
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Quizizz Content
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Mathematics
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11th Grade - University
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Hard
The video tutorial explains why direct substitution cannot be used when evaluating the limit of a function as x approaches 2 due to a zero in the denominator, making the function undefined. The instructor demonstrates how to simplify the expression by factoring the numerator and denominator, allowing the limit to be evaluated as x approaches 2. The result is a hole in the graph, and the limit is calculated to be 5. The lesson concludes with a reminder about the test's free response portion and an optional graph confirmation.
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5 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Because it results in a zero in the numerator
Because it makes the function undefined
Because it simplifies the function
Because it changes the limit
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical technique is suggested to simplify the problem when direct substitution fails?
Completing the square
Factoring
Integration
Differentiation
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplified expression for the limit as X approaches 2?
X - 2
X - 3
X + 2
X + 3
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the term used to describe the point where the function is not defined but the limit exists?
Asymptote
Discontinuity
Hole
Intercept
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value at the hole for the function as X approaches 2?
5
6
4
3
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