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Lim x->0, sinx/x

  • Thread starter Harmony
  • Start date
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lim sinx/x
x->0

Where x is in degree.

I try using calculator to substitute x with 10^1, 10^2,....10^99, and I found that 10^1 to 10^97 give almost the same result, but it suddenly becomes zero from 10^98 onwards. I can get the limit if x is in radian, but how about degree?

p/s : By the way, how do I type the above question in latex?
 
Last edited:

Answers and Replies

VietDao29
Homework Helper
1,417
1
lim sinx/x
x->0

Where x is in degree.

I try using calculator to substitute x with 10^1, 10^2,....10^99, and I found that 10^1 to 10^97 give almost the same result, but it suddenly becomes zero from 10^98 onwards. I can get the limit if x is in radian, but how about degree?

p/s : By the way, how do I type the above question in latex?
Err, is it x tends to 0, or x tends to infinity? :bugeye: The problem seems to ask you to find the limit as x -> 0 (x in degrees), so you can change x from degrees to radians, and use the famous limit: [tex]\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1 \quad (x \mbox{ in radians})[/tex] to complete the problem.
So, we have:
[tex]\lim_{x \rightarrow 0} \frac{\sin x}{x} \quad (x \mbox{ in degrees}) = \lim_{x \rightarrow 0} \frac{\sin \left( \frac{\pi}{180} x \right)}{x} = ...[/tex].
Can you go from here? :)
 
Gib Z
Homework Helper
3,344
4
Btw The reason the calculator tripped up is because it stores say, very small numbers, 0.000000001. But when the number it is storing is too small, and its memory can not fit all the digits, it will get rounded, in this case to zero. Thats your problem.
 

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