Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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.. Consider the following true statement:
"If fix) is differentiable at x=a, then flx) is continuous atx=a." Is the
reasoning below, correct or incorrect? Whyor why not?
x2 + 1
(A) Thefunctionf(x)=
isnotcontinuousatx=2, therefore itcannotbe differentiable atx=2.
x- 2
(B) The function f(x) = |x-5| isnot differentiable atx=5, therefore it cannot be continuous at x=5.
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Transcribed Image Text:.. Consider the following true statement: "If fix) is differentiable at x=a, then flx) is continuous atx=a." Is the reasoning below, correct or incorrect? Whyor why not? x2 + 1 (A) Thefunctionf(x)= isnotcontinuousatx=2, therefore itcannotbe differentiable atx=2. x- 2 (B) The function f(x) = |x-5| isnot differentiable atx=5, therefore it cannot be continuous at x=5.
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