Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
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Math4303Sec4_1Homework Protected View - Saved to this PC - O Search gn Layout References Mailings Review View Help e Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. Enable Editing Math 4303 Homework Section 4.1 Convergence 1. Write out the first seven terms of the sequence dn 2n +1 %3D 3n-1 2. Using only Definition 4.1.2 (N-ɛ definition of convergence), prove the following: k a] lim - = 0 kER 4n +1 b] lim no n+3 = 4 6n? +3n = 3 no 2n? -5 c] lim sin( n) =D0 d] lim 3. Prove or provide a counterexample for the following: a] If (s,) converges then (s) converges. b] If (s,) converges then (s,) converges. c] lim s, = 0 iff lim |s„ =0 4. Suppose that lim s, =0 and suppose that (t, ) is a bounded sequence. Show that lim s,t, = 0 5. Suppose that (x,), (y, ), and (=,) are sequences such that x, Sy, S=, n and lim x, = L = lim = Show that lim y, = L 6. Suppose that lim s. =s where s > 0. Prove that there exists a natural number N, such that if n> N, then s, > 0 DFocus DELL
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Transcribed Image Text:Math4303Sec4_1Homework Protected View - Saved to this PC - O Search gn Layout References Mailings Review View Help e Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. Enable Editing Math 4303 Homework Section 4.1 Convergence 1. Write out the first seven terms of the sequence dn 2n +1 %3D 3n-1 2. Using only Definition 4.1.2 (N-ɛ definition of convergence), prove the following: k a] lim - = 0 kER 4n +1 b] lim no n+3 = 4 6n? +3n = 3 no 2n? -5 c] lim sin( n) =D0 d] lim 3. Prove or provide a counterexample for the following: a] If (s,) converges then (s) converges. b] If (s,) converges then (s,) converges. c] lim s, = 0 iff lim |s„ =0 4. Suppose that lim s, =0 and suppose that (t, ) is a bounded sequence. Show that lim s,t, = 0 5. Suppose that (x,), (y, ), and (=,) are sequences such that x, Sy, S=, n and lim x, = L = lim = Show that lim y, = L 6. Suppose that lim s. =s where s > 0. Prove that there exists a natural number N, such that if n> N, then s, > 0 DFocus DELL
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