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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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My questions are: •What is Xn? ・Why lim n→∞{f(Xn)} ≦lim n→∞{g(Xn)}?Any Thm about sequences?
imil ov 2.5 THEOREM Suppose f :D R and g : D R, xo is an accumulation point of D, and f and g have limits at xo. If f(x) < g(x) for all x E D, then lim f(x) < lim g(x). Xー→X0 Oxt-x
Transcribed Image Text:imil ov 2.5 THEOREM Suppose f :D R and g : D R, xo is an accumulation point of D, and f and g have limits at xo. If f(x) < g(x) for all x E D, then lim f(x) < lim g(x). Xー→X0 Oxt-x
20. Prove Theorem 2.5: Suppose f : D → R and g : D → R, xo is an accumulation point of D, and f and g have limits at xo. If f(x)< g(x) for all x € D, then lim f(x) < lim g(x). Then {f(xn)}1 Let {xn}=1 be a sequence of points in D coverging to xo . converges to lim,-zo f(x), and {g(xn)}1 converges to lim,-zo 9(x). Applying a previous result about sequences gives lim f(x) = lim {f(xn)} < lim {g(x,n)} = lim g(x). n-00
Transcribed Image Text:20. Prove Theorem 2.5: Suppose f : D → R and g : D → R, xo is an accumulation point of D, and f and g have limits at xo. If f(x)< g(x) for all x € D, then lim f(x) < lim g(x). Then {f(xn)}1 Let {xn}=1 be a sequence of points in D coverging to xo . converges to lim,-zo f(x), and {g(xn)}1 converges to lim,-zo 9(x). Applying a previous result about sequences gives lim f(x) = lim {f(xn)} < lim {g(x,n)} = lim g(x). n-00
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