$maple |\^/| Maple 10 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > evalf((10^10)^(10^(-10)),20); 1.0000000023025850956Was that difficult?
I was asked by several people if the sketch could be gotten from the output of a calculator. Sure, I replied, sure. But think about it. Maybe, just maybe, your calculator is misleading you. A calculator computes some values and then, with the help of your eyes and brain, connects the dots.
Look at the picture below. Maybe the true curve is in light blue and somewhat complicated. The calculator has computed the blobby red dots as sample points. Then you, together with the calculator, believe that the curve is the light red object. What's correct?
Therefore you, using calculus, should be prepared to justify the shape of any curve you draw: yes, the calculator certainly may provide supporting evidence, but you need to justify your assertions (using calculus this won't be very difficult!). You should learn to think about the output of "intelligent" machines.
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