grillo's pickle de gallo - GetMeFoodie

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📰 Question: Define $ L(u) = u - rac{u^3}{6} $ for all real $ u $. If $ n $ is a positive integer, define $ a_n $ by $ a_1 = rac{\pi}{2} $, $ a_{n+1} = L(a_n) $. Find $ \lim_{n o \infty} a_n $. 📰 Solution: The recurrence $ a_{n+1} = a_n - rac{a_n^3}{6} $ resembles the Taylor series for $ rctan(u) $, where $ rac{d}{du} rctan(u) = rac{1}{1 + u^2} $. However, the recurrence is not exact. Assume the limit $ L $ exists. Then $ L = L - rac{L^3}{6} \Rightarrow rac{L^3}{6} = 0 \Rightarrow L = 0 $. To confirm convergence, note $ a_1 = \pi/2 pprox 1.57 > 1 $, and $ a_{n+1} = a_n(1 - rac{a_n^2}{6}) $. Since $ a_1 < \sqrt{6} $, $ a_n $ is decreasing and bounded below by 0. By monotone convergence, $ a_n o 0 $. 📰 Question: Find the center of the hyperbola $ 4x^2 - 12x - 9y^2 + 18y = 27 $. 📰 Bank Of America Home Equity Loan 📰 Tsc Credit Card 📰 Bank Of America Logins 📰 Whats Blowing Up The Market Discover The Hottest Clicker Games You Cant Ignore 1410942 📰 Bank America Sign On 📰 Best Banks For Small Business Accounts 2685567 📰 They Said Id Lose My Tracksbut This Song Transfer Pack Rediscovered Me 3989981 📰 Stop Mouse Jitters In Their Tracks Decrease Sensitivity Like A Pro Today 8422216 📰 Top Yahoo Biggest Gainers Shocked Marketsheres Who Outperformed Everything 4459296 📰 Capital To Invest 📰 Friend Apps 📰 Banco Estado 📰 How Much Will It Cost To Build A House 📰 Veeva Systems Stock 📰 72 Equiv 9 4707601