Math problem where graphing calculator may slow you down...

08182014, 09:47 PM
Post: #10




RE: Math problem where graphing calculator may slow you down...
(08172014 10:25 PM)Bunuel66 Wrote: Nothing more than a pen, a 'small' paper and the first scientific calculator you can grasp around you Here's how you can figure out with a 4banger whether \(e^{\frac{5}{4}\pi} > 50\): AC 3.141592654 ÷ 1024 + 1 = × = × = × = × = × = × = × = × = M+ × = × = × MR = The result is: 50.44976377 As \((1+\frac{x}{n})^n \leq e^x\), we can conclude that indeed: \[ \begin{align} 50 & < 50.44976377 \doteq (1+\frac{\pi}{1024})^{1024+256} \\ & = (1+\frac{\pi}{1024})^{1024 \times 1.25} \\ & = ((1+\frac{\pi}{1024})^{1024})^{1.25} \\ & \leq (e^\pi)^{1.25} \\ & = e^{\pi \times 1.25} \\ & = e^{\frac{5}{4}\pi} \end{align} \] Cheers Thomas 

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