for every Suppose f: (0, ∞) → (0, ∞) is defined by f(x)=√ positive real number x. Consider the following proposed proof that f is a continuous function. Let cand & be arbitrary positive real numbers. Then |x - c √x + √c |f(x) = f(c)| = |√x - √√C| = = If 8 is defined as &√c, then f(x) f(c)| < € when x - c < 8. - VI |xc| Ve Which one of the following statements best describes this proposed proof? The proof is valid. The proof is faulty because & is not allowed to depend on c. The proof is faulty because the denominator might be equal to zero. The proof is faulty because the displayed equation is wrong. The proof is faulty because & is not allowed to depend on €.
for every Suppose f: (0, ∞) → (0, ∞) is defined by f(x)=√ positive real number x. Consider the following proposed proof that f is a continuous function. Let cand & be arbitrary positive real numbers. Then |x - c √x + √c |f(x) = f(c)| = |√x - √√C| = = If 8 is defined as &√c, then f(x) f(c)| < € when x - c < 8. - VI |xc| Ve Which one of the following statements best describes this proposed proof? The proof is valid. The proof is faulty because & is not allowed to depend on c. The proof is faulty because the denominator might be equal to zero. The proof is faulty because the displayed equation is wrong. The proof is faulty because & is not allowed to depend on €.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:for every
Suppose f: (0, ∞) → (0, ∞) is defined by f(x)=√
positive real number x. Consider the following proposed proof that f is a
continuous function.
Let cand & be arbitrary positive real numbers. Then
|x - c
√x + √c
|f(x) = f(c)| = |√x - √√C| =
=
If 8 is defined as &√c, then f(x) f(c)| < €
when x - c < 8.
-
VI
|xc|
Ve
Which one of the following statements best describes this proposed
proof?
The proof is valid.
The proof is faulty because & is not allowed to depend on c.
The proof is faulty because the denominator might be equal to zero.
The proof is faulty because the displayed equation is wrong.
The proof is faulty because & is not allowed to depend on €.
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