Show that lim (x³ - x) = 6 in the following steps. Do not use derivatives. x→2 (a) Show: if x - 2| < 1, then |x³ − x − 6| ≤ 18.
Show that lim (x³ - x) = 6 in the following steps. Do not use derivatives. x→2 (a) Show: if x - 2| < 1, then |x³ − x − 6| ≤ 18.
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:Show that lim (x³ - x) = 6 in the following steps. Do not use derivatives.
x-2
(a) Show: if x - 2| < 1, then |x³ – x − 6| ≤ 18.
Transcribed Image Text:(b) Now show, using part (a) and the e-6 - definition of the limit, that lim (x³ - x) = 6.
x-2
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Step 1: Define limit of a function at a point
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