Explain the meaning of the following equation. lim f(x) = 7 X→ 4 O If x₁ - 41 < x₂ − 4], then [f(x₁) — 7|≤ f(x₂) — 7|. O f(x) = 7 for all values of x. O If x₁ - 41 < x₂ - 41, then [f(x₁) - 7| < |f(x₂) - 71. The values of f(x) can be made as close to 7 as we like by taking x sufficiently close to 4. The values of f(x) can be made as close to 4 as we like by taking x sufficiently close to 7. Is it possible for this statement to be true and yet f(4) = 1? Explain. Yes, the graph could have a hole at (4, 7) and be defined such that f(4) = 1. Yes, the graph could have a vertical asymptote at x = 4 and be defined such that f(4) = 1. O No, if f(4) = 1, then lim f(x) = 1. X→ 4 No, if lim f(x) = 7, then f(4) = 7. X→ 4
Explain the meaning of the following equation. lim f(x) = 7 X→ 4 O If x₁ - 41 < x₂ − 4], then [f(x₁) — 7|≤ f(x₂) — 7|. O f(x) = 7 for all values of x. O If x₁ - 41 < x₂ - 41, then [f(x₁) - 7| < |f(x₂) - 71. The values of f(x) can be made as close to 7 as we like by taking x sufficiently close to 4. The values of f(x) can be made as close to 4 as we like by taking x sufficiently close to 7. Is it possible for this statement to be true and yet f(4) = 1? Explain. Yes, the graph could have a hole at (4, 7) and be defined such that f(4) = 1. Yes, the graph could have a vertical asymptote at x = 4 and be defined such that f(4) = 1. O No, if f(4) = 1, then lim f(x) = 1. X→ 4 No, if lim f(x) = 7, then f(4) = 7. X→ 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Explain the meaning of the following equation.
lim f(x) = 7
X→ 4
-
O If x₁ - 41 < x₂ − 4], then [f(x₁) − 7|≤ [f(x₂) — 7|.
O f(x) = 7 for all values of x.
O If x₁ - 41 < x₂ − 4], then [f(x₁) − 7| < |f(x₂) − 7|.
The values of f(x) can be made as close to 7 as we like by taking x sufficiently close to 4.
O The values of f(x) can be made as close to 4 as we like by taking x sufficiently close to 7.
Is it possible for this statement to be true and yet f(4) = 1? Explain.
Yes, the graph could have a hole at (4, 7) and be defined such that f(4) = 1.
Yes, the graph could have a vertical asymptote at x = 4 and be defined such that f(4)
= 1.
No, if f(4) = 1, then lim f(x) = 1.
X→ 4
No, if lim f(x) = 7, then f(4) = 7.
X→ 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9763047e-9567-4a9b-b6af-b6a297414ad2%2F2f393489-71c6-4f52-90e5-aac49c722b23%2Fb9o5s8_processed.png&w=3840&q=75)
Transcribed Image Text:Explain the meaning of the following equation.
lim f(x) = 7
X→ 4
-
O If x₁ - 41 < x₂ − 4], then [f(x₁) − 7|≤ [f(x₂) — 7|.
O f(x) = 7 for all values of x.
O If x₁ - 41 < x₂ − 4], then [f(x₁) − 7| < |f(x₂) − 7|.
The values of f(x) can be made as close to 7 as we like by taking x sufficiently close to 4.
O The values of f(x) can be made as close to 4 as we like by taking x sufficiently close to 7.
Is it possible for this statement to be true and yet f(4) = 1? Explain.
Yes, the graph could have a hole at (4, 7) and be defined such that f(4) = 1.
Yes, the graph could have a vertical asymptote at x = 4 and be defined such that f(4)
= 1.
No, if f(4) = 1, then lim f(x) = 1.
X→ 4
No, if lim f(x) = 7, then f(4) = 7.
X→ 4
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