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Solve this faster with the right shortcut first
Shortcut used: Check direct substitution first; then factor, rationalize, compare one-sided limits, or apply a standard theorem.
Solve in 3 steps:
- Mark the given values and the exact target.
- Apply the relevant formula, rule, or concept.
- Check the final value against the options.
Common mistake: Do not choose an option before confirming the exact demand of the question.
Question 9
Multiple Choice Question
Question
A table gives f(1.9)=4.61, f(1.99)=4.9601, f(2.01)=5.0401, and f(2.1)=5.41. Which value is the best estimate of lim(x→2)f(x)?
Explanation
Correct Answer: A
ANSWER
Correct Answer: A
Method / Topic: Limits
Values from both sides approach 5 as x approaches 2.
Why this answer is correct
The correct option matches the required rule and the given information.
Short Explanation
Values from both sides approach 5 as x approaches 2.
Detailed Explanation
Question
A table gives f(1.9)=4.61, f(1.99)=4.9601, f(2.01)=5.0401, and f(2.1)=5.41. Which value is the best estimate of lim(x→2)f(x)?
ANSWER
Correct Answer: A
Method / Topic: Limits
Values from both sides approach 5 as x approaches 2.
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Question 9
Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake
Learn + solve
Shortcut used, common trap, and the fastest solving route
Shortcut used: Check direct substitution first; then factor, rationalize, compare one-sided limits, or apply a standard theorem.
Solve in 3 steps:
- Mark the given values and the exact target.
- Apply the relevant formula, rule, or concept.
- Check the final value against the options.
Common mistake: Do not choose an option before confirming the exact demand of the question.
Question
A table gives f(1.9)=4.61, f(1.99)=4.9601, f(2.01)=5.0401, and f(2.1)=5.41. Which value is the best estimate of lim(x→2)f(x)?
Explanation
Correct Answer: A
ANSWER
Correct Answer: A
Method / Topic: Limits
Values from both sides approach 5 as x approaches 2.
Why this answer is correct
The correct option matches the required rule and the given information.
Short Explanation
Values from both sides approach 5 as x approaches 2.
Detailed Explanation
Question
A table gives f(1.9)=4.61, f(1.99)=4.9601, f(2.01)=5.0401, and f(2.1)=5.41. Which value is the best estimate of lim(x→2)f(x)?
ANSWER
Correct Answer: A
Method / Topic: Limits
Values from both sides approach 5 as x approaches 2.
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Concept tagged
Check direct substitution first; then factor
rationalize
compare one-sided limits
or apply a standard theorem.