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Limit of 2x/(x-7) as x approaches 7 from the right
Published on October 17, 2024
Calculus
The limit of (2x)/(x-7) as x approaches 7 from the right is positive infinity.
Question
Answer
We need to evaluate the limit:
1. Direct Substitution:
- If we directly substitute x = 7 into the expression, we get a 0 in the denominator, which is undefined. This tells us we need to investigate further.
2. Analyzing the Behavior:
- Numerator: As x approaches 7 from the right (x → 7+), the numerator (2x) approaches 14.
- Denominator: As x approaches 7 from the right (x → 7+), the denominator (x - 7) approaches 0. However, since x is slightly larger than 7, the denominator will be a very small positive number.
3. Determining the Limit:
- We have a situation where the numerator approaches a constant (14) and the denominator approaches a very small positive number. This means the fraction will become very large and positive.
Therefore:
The answer is (A).