An Elusive Limit Question 6: Subtracting Nearly Identical Numbers can BREAK Calculators!

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In this video I explain that the reason calculators gave an unclear limit for the complicated trigonometric function is because every term was nearly identical, to the point where subtracting them resulted in a difference too small for the precision of most calculators. The calculator would then have to round up or down, which can give the wrong answer. For example 1.0000000000123 - 1 = 0.0000000000123. If a calculator doesn't have more than 10 digits of precision, the difference would be rounded up to 0. And if this was in the numerator, as in the limit, then we obtain an indeterminate or undefined form of number / 0.

I also illustrate this by graphing the function and every term of it in Desmos graphing calculator. I zoom in beyond the precision of most calculators yet the terms still appear identical: https://www.desmos.com/calculator/vhwpqsail1

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