See the attachment. Please answer the question with all processes and detailed explanation. And please meet the requirements. 2. Prove, using the ε-8 definition of continuity that the functionx²5x-9ƒ : R\{}} → R defined by ƒ(x) ==is continuous at xo=2.

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Answered: ƒ:R\{}} → R defined by f(x) = x² 5x-9…

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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See the attachment. Please answer the question with all processes and detailed explanation. And please meet the requirements.

2. Prove, using the ε-8 definition of continuity that the function
x²
5x-9
ƒ : R\{}} → R defined by ƒ(x) =
=
is continuous at xo
=
2.

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Is this a mistake? Because the middle term in the inequality is 5 epsilon times a number which is bigger than 1. Then 5 epsilon should be smaller. And I don't really understand the inequality in step 3, for example, if we let x=17, then the numerator will be positive while we get a negative denominator. The result will be negative, that is smaller than 1.