Toxic's blog

By Toxic, 8 years ago, translation, In English

Hello! I have a question: how to find value of , if we know value of and we shouldnt find x, because it may be very-very big? Is it impossible?

 
 
 
 
  • Vote: I like it
  • +8
  • Vote: I do not like it

»
8 years ago, # |
Rev. 2   Vote: I like it -31 Vote: I do not like it

UPD: Это разные функции, но ничего. Уверен, они дают повод для размышлений.

»
8 years ago, # |
  Vote: I like it +41 Vote: I do not like it

for very large x.

Of course, if x is very-very big, then up to precision of your data types, the difference is negligible (if is in the order of 103, is in the order of 10 - 400) and you can just write .

  • »
    »
    8 years ago, # ^ |
      Vote: I like it +44 Vote: I do not like it

    It can be shown that error is asymptotically small enough.

    (Mean value theorem)

    Thus if x if large enough you may say that and get the error of order not more than O(1 / x2).

  • »
    »
    8 years ago, # ^ |
      Vote: I like it +35 Vote: I do not like it

    Actually you could take first k elements of Taylor series and precision will be