Lim x->0 | sinx/x | in Degrees

  • Thread starter Harmony
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In summary, when finding the limit of sinx/x as x approaches 0 in degrees, it is equivalent to finding the limit in radians using the formula \lim_{x \rightarrow 0} \frac{\sin x}{x} = 1. This is because the calculator may round the number to zero due to its limited memory.
  • #1
Harmony
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0
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?
 
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  • #2
Harmony said:
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? :)
 
  • #3
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.
 

1. What is the value of lim x->0 | sinx/x | in degrees?

The value of lim x->0 | sinx/x | in degrees is equal to 1 degree. This is because as x approaches 0, the value of sinx/x also approaches 1.

2. How does the value of lim x->0 | sinx/x | in degrees compare to its value in radians?

The value of lim x->0 | sinx/x | in degrees is equal to the value of lim x->0 | sinx/x | in radians. This is because the trigonometric functions remain the same regardless of the unit of measurement used.

3. What does the graph of lim x->0 | sinx/x | in degrees look like?

The graph of lim x->0 | sinx/x | in degrees resembles a straight line with a slope of 1 from the positive x-axis to the origin. It then curves sharply upwards towards the positive y-axis.

4. How do you calculate the value of lim x->0 | sinx/x | in degrees?

The value of lim x->0 | sinx/x | in degrees can be calculated by plugging in 0 for x in the function and evaluating the resulting expression. In this case, the value would be equal to 1.

5. What real-life applications does lim x->0 | sinx/x | in degrees have?

Lim x->0 | sinx/x | in degrees has various real-life applications in fields such as physics, engineering, and computer science. For example, it is used in the calculation of limits and derivatives, as well as in the analysis of oscillating systems and signal processing.

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