When using a graphing utility to generate a table, I got 0.01745 as the limit rather than 1. Where did I go wrong?
I calculated $\lim_{x\to 0} {\sin x\over x}$ as 0.01745 instead of 1
4
$\begingroup$
calculus
limits
numerical-methods
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2Can you post the table? How small of values did you use for $x$? – 2012-09-10
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6Were you possible in the wrong mode? Degrees vs. radians. – 2012-09-10
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3When you used degrees instead of radians. Reset your calculator to radians, and it all works out. – 2012-09-10
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2You made the _usual_ mistake. – 2012-09-10
1 Answers
18
Your calculator was in the wrong mode. You need to be in radians for most formulae to hold regarding trig functions. Once you switch it into radians, your table should be fine - showing that the limit is indeed $1.$
Fun fact: If you were in degrees, the limit should come out to $\frac{\pi}{180} \approx .01745$ which is what you had.
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0Ah, nice catch! – 2012-09-10