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5. Compute the maximum, minimum, in fimum and supremum (whenever these exist) for the following sets, (i) {1+ 1+(-1)" :n e N} (ii) {x : x € Q and x² < 2} 6. Use the c- definition of limits of a sequence to cstablish the following limits (i) lim,+∞(,) = 0 (ii) lim,,+∞12) = 3 n+00 n+1 (iii) If a > 0 then lim,, yo0(na) = 0

5. Compute the maximum, minimum, in fimum and supremum (whenever these exist) for the following sets, (i) {1+ 1+(-1)" :n e N} (ii) {x : x € Q and x² < 2} 6. Use the c- definition of limits of a sequence to cstablish the following limits (i) lim,+∞(,) = 0 (ii) lim,,+∞12) = 3 n+00 n+1 (iii) If a > 0 then lim,, yo0(na) = 0

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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5. Compute the marimum, minimum, in fimum and supremum (whenever these exist) for the following sets, (i) {1+ 1+(-1)" :n e N} (ii) {x : x E Q and x² < 2} 6. Use the c- definition of limits of a sequence to establish the following limits (i) lim,-0o („) = 0 (ii) lim,,+(2) = 3 %3D n+00 n+1 n+1 (iii) If a > 0 then lim, 0( 고) = 0 na+1
Transcribed Image Text:5. Compute the marimum, minimum, in fimum and supremum (whenever these exist) for the following sets, (i) {1+ 1+(-1)" :n e N} (ii) {x : x E Q and x² < 2} 6. Use the c- definition of limits of a sequence to establish the following limits (i) lim,-0o („) = 0 (ii) lim,,+(2) = 3 %3D n+00 n+1 n+1 (iii) If a > 0 then lim, 0( 고) = 0 na+1
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