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📰 Solution: To find the maximum value of $ f(t) = t^2 - \frac{t^4}{4} $, take the derivative $ f'(t) = 2t - t^3 $. Set $ f'(t) = 0 $: $ 2t - t^3 = 0 \Rightarrow t(2 - t^2) = 0 $. Critical points at $ t = 0 $ and $ t = \pm\sqrt{2} $. Evaluate $ f(\sqrt{2}) = (\sqrt{2})^2 - \frac{(\sqrt{2})^4}{4} = 2 - \frac{4}{4} = 1 $. The maximum value is $ \boxed{1} $. 📰 Question: A bioinformatician analyzes gene expression levels modeled by $ g(n) = \frac{3n^2 + 5n}{n^2 + 1} $, where $ n $ is the number of samples. Determine the limit of $ g(n) $ as $ n \to \infty $. 📰 Solution: Divide numerator and denominator by $ n^2 $: $ g(n) = \frac{3 + \frac{5}{n}}{1 + \frac{1}{n^2}} $. As $ n \to \infty $, $ \frac{5}{n} \to 0 $ and $ \frac{1}{n^2} \to 0 $. Thus, the limit is $ \frac{3}{1} = \boxed{3} $. 📰 Dailypay App Breaks Payment Barrierssee How It Revolutionizes Your Income 2525418 📰 Madison Town Center Apartments Madison Al 4029660 📰 Skyrim Ebony Blade 📰 Bob Dylan And Joan Baez 📰 Investigation Begins View Net Framework Version And Everyone Is Talking 📰 Margaritaville San Diego 606244 📰 You Wont Believe What This Salmo 91 Catlico Can Doyou Must Try It 2917755 📰 Medium React 6308207 📰 Avg Antivirus Software For Android 📰 Emergency Alert Wells Fargo Signify Business Credit Card And The Investigation Deepens 📰 Major Breakthrough Imei Check Verizon And The World Watches 📰 Complete Reasons Why Why Isnt Is Silently Sabotaging You 9861880 📰 Uae Dirham In Euro 📰 Anthony Edwards Shoes 2616620 📰 Live The Dream In Secluded Forest Park Apartments You Never Thought Ownable 566165