The graph of f(x) is shown (see figure). 6x f(x): = x² + 1 (a) Find the following limits. L = lim f(x) = 6 x → ∞0 K= lim f(x) = X→-00 (b) Determine X₁ and X₁ x₂ || -6 || x2 X X Not drawn to scale in terms of ε. (c) Determine M, where M > 0, such that If(x) — L| < ε for x > M. M (d) Determine N, where N < 0, such that If(x) - K| < ε for x < N. N = ||

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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The graph of f(x) is shown (see figure).
6x
√x² +1
f(x) =
(a) Find the following limits.
L= = lim f(x) =
6
x → 00
K = lim f(x) = -6
X→-00
X₁
=
(b) Determine X₁ and x₂ in terms of ε.
X2
II
||
Not drawn to scale
(c) Determine M, where M > 0, such that If(x) - L < & for x > M.
M =
X
(d) Determine N, where N < 0, such that If(x) - K| < & for x < N.
N = ||
X
Transcribed Image Text:The graph of f(x) is shown (see figure). 6x √x² +1 f(x) = (a) Find the following limits. L= = lim f(x) = 6 x → 00 K = lim f(x) = -6 X→-00 X₁ = (b) Determine X₁ and x₂ in terms of ε. X2 II || Not drawn to scale (c) Determine M, where M > 0, such that If(x) - L < & for x > M. M = X (d) Determine N, where N < 0, such that If(x) - K| < & for x < N. N = || X
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