Cant understand the question

  • Thread starter nhrock3
  • Start date
Without additional explanation, it is not clear how this relates to the original question. It seems that the equation is meant to show that the error or difference between e^x and e^{[x]} e^{x-[x]} is small or negligible. However, it is not clear why this is the case or how it is relevant to the larger context. In summary, the question is asking about the accuracy of e^x in a computer and how the equation e^x=e^{[x]}e^{x-[x]} relates to a "fraction" or possibly an error in the calculation. The equation seems to show that the error or difference between e^x and e^{[
  • #1
nhrock3
415
0
the question is stated as such
"number 'e' is found almost accurately in a certain computer,and we can consider it as accurate.so each power of it also accurate. so we left to calculate the fracture ie
[tex]e^x=e^{[x]}e^{x-[x]}[/tex] "the question goes on

how is [tex]e^x=e^{[x]}e^{x-[x]}[/tex] a fracture
?
square cols represent the whole value
 
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  • #2
There may be a language problem here. I think that, instead of "fracture" you mean "fraction" or possibly just "error"?
 
  • #3
yes fraction
how its fraction
 
  • #4
Without additional explanation, your notation is not very clear. By [x], I think you mean the floor of x, or [itex]\left\lfloor x \right\rfloor[/itex]. The floor of x is the largest integer that is less than or equal to x. E.g., [itex]\left\lfloor 2.7 \right\rfloor = 2[/itex].

Using x = 2.7 in your equation, we have
[tex]e^x = e^{\left\lfloor 2.7 \right\rfloor}e^{2.7 - \left\lfloor 2.7 \right\rfloor }[/tex]
[tex]= e^2 e^{2.7 - 2} = e^2 e^{.7}[/tex]
 

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