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Use the Squeeze Theorem to show that lim (x² cos 5x) = 0. Illustrate by graphing the functions f(x) = -x², g(x) = x² cos 5x, and h(x) = x² on the same screen. x → 0 < x² cos 5πx Let f(x) = -x², g(x) = x² cos 5πx, and h(x) = x². Then? ≤cos 5πx ≤ v → ? ? ? g(x) f(x) h(x) V Since lim f(x) = lim h(x) = | X-0 0+x by the Squeeze Theorem we have lim g(x) = X+0 ? -1 0 1

Use the Squeeze Theorem to show that lim (x² cos 5x) = 0. Illustrate by graphing the functions f(x) = -x², g(x) = x² cos 5x, and h(x) = x² on the same screen. x → 0 < x² cos 5πx Let f(x) = -x², g(x) = x² cos 5πx, and h(x) = x². Then? ≤cos 5πx ≤ v → ? ? ? g(x) f(x) h(x) V Since lim f(x) = lim h(x) = | X-0 0+x by the Squeeze Theorem we have lim g(x) = X+0 ? -1 0 1

Advanced Engineering Mathematics
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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2.3 Q13

Use the Squeeze Theorem to show that lim (x² cos 5x) = 0. Illustrate by graphing the functions f(x) = -x², g(x) = x² cos 5x, and h(x) = x² on the same screen. x → 0 < x² cos 5πx Let f(x) = -x², g(x) = x² cos 5πx, and h(x) = x². Then? ≤cos 5πx ≤ v → ? ? ? g(x) f(x) h(x) V Since lim f(x) = lim h(x) = | X-0 0+x by the Squeeze Theorem we have lim g(x) = X+0
Transcribed Image Text:Use the Squeeze Theorem to show that lim (x² cos 5x) = 0. Illustrate by graphing the functions f(x) = -x², g(x) = x² cos 5x, and h(x) = x² on the same screen. x → 0 < x² cos 5πx Let f(x) = -x², g(x) = x² cos 5πx, and h(x) = x². Then? ≤cos 5πx ≤ v → ? ? ? g(x) f(x) h(x) V Since lim f(x) = lim h(x) = | X-0 0+x by the Squeeze Theorem we have lim g(x) = X+0
? -1 0 1
Transcribed Image Text:? -1 0 1
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