
number 4 Ex. 3.1. Determine, when possible, the function f(x) to which the following sequences converge...
Problem #10: Which of the following sequences converge? (i) an (-1)n+1 n n2 - 7 (-1)" n2 n? - (iii) an = cos(NT) (iv) an= sin(nn) (ii) an= -9 (A) (i) only (B) (ii) only (C) (i) and (iv) only (D) (i) and (iii) only (E) (ii) and (iii) only (F) (ii) and (iv) only (G) all of them (H) none of them
number 4 as clearly as possible
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series...
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NUMBER 3 (Parts A-F)
Consider the following list of properties 3. f(x)oo x-+1 ii) lim()2 iv) f(1)-3 v) lim f(x)-n x+1 For each of the following, decide if it is possible for a function to have the given set of properties. If so, sketch and label a possible graph for the function on the axis provided. If no such function is possible, explain why not. a) (i) and (i) b) (), (ii), and (iv) c) (i), (iii),...
question 17
Determine which of the following relation(s) represent a function: I.y = 5 II. x² + y = 9 III. x² + y2 = 7 IV. y = |x] – 5 V.x=1 VI. x = lyſ + 7 a) I, II, IV only b) O II, IV, V only c) O II, III, IV only d) OI, IV, VI only e) OI, V, VI only
number 4
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
(35 pls) Determine if each of the following seven series converge or diverge. Do not use a test for convergence or a test for divergence more than once. If you use the Integral Test, do not bother to show me that you checked the three prerequisites to that test. i) 2(04-) n.1 ii) (-1)"n(2n)! -1 (n + 1) (2n) 21 n=1 n 3 iii) 2+ n-1 iv) n=0 1+en 00 1 v) n-07T +n* vi) (-1)"e" 1+en n=0 vii) Ž(-1)"...
3.5.7 (a,c)
3.5.6. Does the sequence , (c) = nxen converge pointwise to the zero function for x E R? Does it converge uniformly? 3.5.7. Answer Exercise 3.5.6 when S 1. n< <n +1, (a) u (c) = xe (b) un() = 0, otherwise, S1, n<<n +1/n, (d) vn(x) = S 1/n, 1<x<2n, 10, otherwise, S 1/n, n<3 <2n, - nc-1, -1/n <3 <1/n, (e) Ur (20) = { 10, otherwise, otherwise. (c) un 10, otherwise, i u n ,...
a) Given 20.00 mL of 0.2000 M diethylamine (CH3CH2)2NH (Kb = 3.1 x 10-4), determine the pH for the titration against 0.1000 M Hal at the following HCl volumes: i) 0.0 mL, ii) 1/4 eq pt, iii) 15.00 mL, iv) 20.00 mL, v) 3/4 eq pt, vi) 35.00 mL, vii) at the eq pt, viii) 50.00 mL, ix) 20.00 mL beyond the eq point. b) Use the results of part 'a' to sketch the titration curve. Make the line as...
3 only
Ex. 3.2. Determine the values of x € R for which the following series con- verge pointwise. 2η (1) Σ2nα (ii) 2η 1+ 2η (2+1)2η n=0 n=0. Με Με Με n=0 | 3η (8) Σ" hete") (vi) Σ. (vii) Σ α ” ln(") n=1 (1) Σεπ 1η-2η 1+0202 = 1
high light only
Ex. 3.2. Determine the values of x E R for which the following series con- verge pointwise. n=0 η (2n+1) in Inn n=0 n=0 n=1 (0) Σαλαθι «Σανα) (0) Σαπουν (0 ΣΗ(el) (Σ. ΘΣτε X η • n=1 n=1 n=0.