Use the Squeeze Theorem to show that lim x2 co X-0 cos(207TX) = 0. Illustrate by graphing the functions f(x) = -x², g(x) = x² cos(207x), and h(x) = x² on the same screen. Let f(x) = -x², g(x) = x² cos(207x), and h(x) = x². Then 0s cos(207x) s 1 f(x)=x² cos(207x)s ? Since lim f(x)= lim h(x)= x-0 x-0 by the Squeeze Theorem we have lim_ g(x)=
Use the Squeeze Theorem to show that lim x2 co X-0 cos(207TX) = 0. Illustrate by graphing the functions f(x) = -x², g(x) = x² cos(207x), and h(x) = x² on the same screen. Let f(x) = -x², g(x) = x² cos(207x), and h(x) = x². Then 0s cos(207x) s 1 f(x)=x² cos(207x)s ? Since lim f(x)= lim h(x)= x-0 x-0 by the Squeeze Theorem we have lim_ g(x)=
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:Use the Squeeze Theorem to show that lim x² cos(207TX) = 0.
X → 0
Illustrate by graphing the functions f(x) = -x², g(x) = x² cos(207x), and h(x) = x² on the same screen.
Let f(x) = -x², g(x) = x² cos(207tx), and h(x) = x². Then [0 ✓≤ cos(207TX) ≤ 1
f(x)
V
≤ x² cos(207Tx) ≤ ?
S
. Since lim f(x) = lim_h(x) :
=
X → 0
X → 0
, by the Squeeze Theorem we have lim g(x)
X → 0
=
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