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CSE 555 Homework One Sample Solutions Let = f˙ 1;PK ;îRÅ ¢ ½ title_pagexhtmlUT Áçî`Áçî`ux !C C C C C C C A ˘2jx¡yj˙2–˙† The reason this sequence doesn't have any uniformly convergent subsequences is that the sequence converges pointwise to 0, so any subsequence must converge pointwise to 0, but fn(n¯ 1 2) ˘1, so if we have some subsequence {fn k} and we set †˙1, then sup x2R jfn k (x)¡ f (x)j‚1 ¨† for all k 5

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‚‰æŽ¿ ƒfƒXƒNƒgƒbƒv pc •ÇŽ† ‚¨‚µ‚á‚ê ƒVƒ"ƒvƒ‹-Title Microsoft Word Solución Pág 40 Y 41 Author afjim Created Date 4/4/ PM4 Consider a series P ∞ n=1 a nLet S n = P n k=1 a k be the nth partial sum and define σ n = P n k=1 S k n We say that the series P ∞ n=1 a n is Cesaro summable to L if limσ n = L A consequence of HW 4 Problem #5 from last semester is that ifP

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;˙ ngbe a nite alphabet, and suppose that the symbols have a total ordering ˙ 1 ˚˙ 2 ˚˚ ˙ nWe say that a string w 1 w m is sorted if w i w i1 for all 1 iMicrosoft Windows f X N g b v T ` ð J n é f X N o Ì \ ¦ Æ ñ \ ¦ ð Ø è Ö ¦ é f X N o I v V ð Ý è é V X e v Windows f X N g b v T ` ð g p µ Ä f ^ ð õ é Web õ ð é õ ê ð Ý è éTitle Microsoft PowerPoint Estimaciones Author afjim Created Date PM

©Dr £1‡ 04@ J (68 c9Ÿ Kµ 4* l} —9W w7Ï PO B9{ I8O ¶7k '5Ä b1 £25 H3 ñ3H N9 9« ‹1¶ 3õ T5" Á8@ >9P ª5" ¥4( Ø3Ë ä/‡ ¾0 †1o ©Eå * ‹0O ÁG ©² t (©{AÜ ¶L NO åMì ÜK` Ð\@ "J« üJ¶ ™e1 GÃ2How many positive integer factors of 9,800,000 are not perfect squares?C 2 – C 1 m = 212 – 32 100 – 0 m = 180 100 = 9 5 Therefore F = 9 5 C b To find b, substitute the coordinates of either point 32 = 9 5 (0) b Therefore b = 32 Therefore the equation is F = 9 5 C 32 Can you solve for C in terms of F?

Æ Ç È É ­ Ê Ë « Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø Å É Ç ¶ ³ ¼ ¸ Õ ª « ¬ ­ Ù ¯ Ú ¼ ¿ É Ç ² ³ ´ º ± ¾ Ø × Å Î ¶ ¸ Ñ È Û ­ Ê Ë « Ì Ü Ý Þ ß à á â ã ä å æ ç è é ê ë Í Ã Å Î ² ì Ð Ô É Ç ¶ Å ¸ ³ ± È ´ ¼ í ² º ½ ¹ Î ¿ î ï ð ñ ¾ ò Æ ó Å É ÇC= b' Then we have c= b'= (ak)'= a(k'), hence ajc To prove (b), suppose that ajband ajc, ie, there exist k;'2Z such that b= akand c= a' Then for any x;y2Z we have bxcy= (ak)x(a')y= a(kxy'), hence aj(bxcy) Finally, we prove (c) We assume that aand bare nonzero, otherwise the whole thing is pretty silly Now suppose3 Given A = {2,1,0,1,2}, show your work and calculate XEA 4 Show the steps to convert this summation into its closed form You may use the summation formulae on page 175 in Table 2 of the textbook as proven identities Always reference any of these identities when you use them (just like we have done

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CS 310 Winter 01 Final Exam (solutions) SOLUTIONS 1 (Logic) Prove the following logical equivalence using truth tables p !242 Solutions SketchthefollowingCartesianproductsonthexy plane 9 { 1,2 3}£{¡1 0 } ¡3 ¡2 ¡1 1 2 3 ¡2 ¡1 1 2 11 0,1 £ ¡3 ¡ 2¡1 1 2 3 ¡2 ¡1 1 2 13EC02 Spring 06 HW3 Solutions 3 Problem 224 • The random variable X has PMF PX (x) = ˆ c/x x = 2,4,8, 0 otherwise (a) What is the value of the constant c?

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B, c, d are in GP and 1/c, 1/d, 1/e are in AP prove that a, c, e are in GP It is given that a, b, c are in AP So, their common difference is same b – a = c – b b b = c a 2b = c a b = (𝑐 𝑎)/2 Also given that b, c, d are in GPCannot be a c satisfying the condition stated in the problem This does not violate the Mean Value Theorem because the function f is not differentiable on (0,3) in particular, it is not differentiable at x = 1/2 2 5 Exercise 4218 Show that the equation 2x−1−sinx = 0 has exactly one real rootTheorem 1 If and then 1 2 Proof and for large Thus, By definition, equation 1 holds Equation 2 can be similarly proved QED 3, , , Notation Conventional Definition ofWesay or is iff there exist positive constants

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 Answers 1 The minimum value is sqrt (5) 2 The minimum value is 36 1 From symmetry, the minimum occurs when OA = OB, where O is the origin The tangent line (touching the circle at T, say) is then at an angle of 45degrees to the horizontal, and 90 degrees to the radial line OT, so forms 45/45/90 right angled triangles with horizontal@ A/V v Z b T I/O v Z b T ́C J E o X 猩 ԂɊe @ \ } b s O 邱 Ƃ CPCI o X Ƀ} b s O 邱 Ƃ \ ł D o X g K v ȃ \ X DMA d l W Ă PCI o X ɁCPCI o X ɐڑ قǍ @ \ ł͂Ȃ \ X(LED o ͂ f B b v X C b ` ) ́C o X E v g R ȒP ȃ J E o X Ɏ Ƃ 悤 ɁC K v ȋ@ \ d l ɂ 킹 Ď R ݂ɃV X e E E } b v ݌v ł ܂ D Free Online Scientific Notation Calculator Solve advanced problems in Physics, Mathematics and Engineering Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History

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