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Mathematical Food For Thought

Mathematical Food For Thought. Saturday, July 7, 2007. Topic: Algebra. Level: AMC/AIME. Given two positive reals $ alpha $ and $ beta $, show that there is a continuous function $ f $ that satisfies $ f(x) = f(x alpha) f(x beta) $. There are several special cases that are interesting to look at before we make a guess as to what type of function $ f $ will be. First we consider the case $ alpha = beta = 1 $. This immediately gives. F(x) = 2f(x 1) $. F(x) = f(x-1) f(x-2) $. F(x) = a x $. Evaluate $ display...

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Mathematical Food For Thought | mathematicalfoodforthought.com Reviews

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Mathematical Food For Thought. Saturday, July 7, 2007. Topic: Algebra. Level: AMC/AIME. Given two positive reals $ alpha $ and $ beta $, show that there is a continuous function $ f $ that satisfies $ f(x) = f(x alpha) f(x beta) $. There are several special cases that are interesting to look at before we make a guess as to what type of function $ f $ will be. First we consider the case $ alpha = beta = 1 $. This immediately gives. F(x) = 2f(x 1) $. F(x) = f(x-1) f(x-2) $. F(x) = a x $. Evaluate $ display...

<META> KEYWORDS

1 whats your function

2 problem

3 solution

4 posted by

5 jeffrey wang

6 6 comments

7 email this

8 blogthis

9 share to twitter

10 share to facebook

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whats your function,problem,solution,posted by,jeffrey wang,6 comments,email this,blogthis,share to twitter,share to facebook,share to pinterest,labels algebra,4 comments,labels calculus,given a,complicated,the adjective,or newton's method,no comments

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Mathematical Food For Thought | mathematicalfoodforthought.com Reviews

https://mathematicalfoodforthought.com

Mathematical Food For Thought. Saturday, July 7, 2007. Topic: Algebra. Level: AMC/AIME. Given two positive reals $ alpha $ and $ beta $, show that there is a continuous function $ f $ that satisfies $ f(x) = f(x alpha) f(x beta) $. There are several special cases that are interesting to look at before we make a guess as to what type of function $ f $ will be. First we consider the case $ alpha = beta = 1 $. This immediately gives. F(x) = 2f(x 1) $. F(x) = f(x-1) f(x-2) $. F(x) = a x $. Evaluate $ display...

INTERNAL PAGES

mathematicalfoodforthought.com

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Mathematical Food For Thought: May 2007

http://www.mathematicalfoodforthought.com/2007_05_01_archive.html

Mathematical Food For Thought. Monday, May 28, 2007. One By One, Were Making It Fun. Topic: Calculus/S&S. Stolz-Cesaro) Let $ {a n } $ and $ {b n } $ be sequences of real numbers such that $ {b n } $ is positive, strictly increasing, and unbounded. If the limit. Displaystyle lim {n rightarrow infty} frac{a {n 1}-a n}{b {n 1}-b n} = L $. Exists, then the following limit also exists and we have. Displaystyle lim {n rightarrow infty} frac{a n}{b n} = L $. The summation we wish to take the limit of is then.

2

Mathematical Food For Thought: Colorful! Topic: Calculus.

http://www.mathematicalfoodforthought.com/2007/06/colorful-topic-calculus_6.html

Mathematical Food For Thought. Wednesday, June 6, 2007. Green's Theorem) Let $ R $ be a simply connected plane region whose boundary is a simple, closed, piecewise smooth curve $ C $ oriented counterclockwise. If $ f(x, y) $ and $ g(x, y) $ are continuous and have continuous first partial derivatives on some open set containing $ R $, then. Displaystyle oint C f(x, y) dx g(x, y) dy = int R int left( frac{ partial g}{ partial x}- frac{ partial f}{ partial y} right) dA $. Then finally we have. Displaystyle...

3

Mathematical Food For Thought: July 2007

http://www.mathematicalfoodforthought.com/2007_07_01_archive.html

Mathematical Food For Thought. Saturday, July 7, 2007. Topic: Algebra. Level: AMC/AIME. Given two positive reals $ alpha $ and $ beta $, show that there is a continuous function $ f $ that satisfies $ f(x) = f(x alpha) f(x beta) $. There are several special cases that are interesting to look at before we make a guess as to what type of function $ f $ will be. First we consider the case $ alpha = beta = 1 $. This immediately gives. F(x) = 2f(x 1) $. F(x) = f(x-1) f(x-2) $. F(x) = a x $. Simple template&#4...

4

Mathematical Food For Thought: March 2007

http://www.mathematicalfoodforthought.com/2007_03_01_archive.html

Mathematical Food For Thought. Saturday, March 31, 2007. Good job to all Bellevue people at MAO State! We placed 3rd in Sweepstakes! That's the highest we've ever gotten in my four years :). Tuesday, March 27, 2007. Condensation Sensation. Topic: Calculus/S&S. Cauchy Condensation Test) If $ displaystyle {a n } {n = 0} { infty} $ is a monotonically decreasing sequence of positive reals and $ p $ is a positive integer, then. Well, let's apply the Cauchy condensation test. Then we know that. Displaystyle su...

5

Mathematical Food For Thought: November 2006

http://www.mathematicalfoodforthought.com/2006_11_01_archive.html

Mathematical Food For Thought. Thursday, November 30, 2006. Exponents Away. Topic: Algebra/Calculus. Level: AIME/Olympiad. 6512) Suppose $ n $ is a nonnegative integer and. F n(x) = c 0e {r 0x} c 1e {r 1x} cdots c ne {r nx} $,. Where $ c i $ and $ r i $ are real numbers. Prove that if $ f $ has more than $ n $ zeros in $ mathbb{R} $, then $ f(x) equiv 0 $. First, we add the claim that $ f n(x) = 1 $ can occur for at most $ n 1 $ distinct $ x $. B 0e {r 0x} b 1e {r 1x} cdots b ke {r kx} = 1 $. Comment: A ...

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Project2020 - High School Math

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Skip to main content. Create interactive lessons using any digital content including wikis with our free sister product TES Teach. Get it on the web. Khan Academy http:/ www.youtube.com/user/khanacademy#g/p. Oswego City School District Regents Exam Prep Center. Algebra http:/ www.regentsprep.org/Regents/math/ALGEBRA/math-ALGEBRA.htm. Geometry http:/ www.regentsprep.org/Regents/math/geometry/math-GEOMETRY.htm. Algebra2/Trig http:/ www.regentsprep.org/Regents/math/algtrig/math-algtrig.htm.

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OverParenting: Resource links for my college prep presentation at Seattle ChineseSchool

http://www.overparenting.com/2010/01/resource-links-for-my-college-prep.html

Good, bad and fun ideas of parenting. Tuesday, January 05, 2010. Resource links for my college prep presentation at Seattle Chinese School. SAT and SAT II: http:/ www.collegeboard.com/student/testing/sat/about.html. ACT: http:/ www.act.org/aap/. PSAT: http:/ www.collegeboard.com/student/testing/psat/about.html. Introducing Score Choice: A New Way to Report Your SAT Scores: http:/ www.collegeboard.com/student/testing/sat/score choice.html. Peterson's guide: http:/ www.petersons.com/. USA Math Olympiad: ht...

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mathematicalfoodforthought.com

Mathematical Food For Thought

Mathematical Food For Thought. Saturday, July 7, 2007. Topic: Algebra. Level: AMC/AIME. Given two positive reals $ alpha $ and $ beta $, show that there is a continuous function $ f $ that satisfies $ f(x) = f(x alpha) f(x beta) $. There are several special cases that are interesting to look at before we make a guess as to what type of function $ f $ will be. First we consider the case $ alpha = beta = 1 $. This immediately gives. F(x) = 2f(x 1) $. F(x) = f(x-1) f(x-2) $. F(x) = a x $. Evaluate $ display...

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