→ yuponkimo : 謝謝! 11/09 12:29
※ 引述《yuponkimo (皇甫尊)》之銘言:
: http://i.imgur.com/NXYqt9R.jpg
: 請問這題要怎麼算啊…
: 怎麼想都想不出來
原式
2sqrt(1/x + sqrt(1/x))
= lim ----------------------------------------------------------------------
sqrt(1/x + sqrt(1/x + sqrt(1/x))) + sqrt(1/x - sqrt(1/x + sqrt(1/x)))
2sqrt(1/x) sqrt(1 + sqrt(x))
= lim -------------------------------------------------
sqrt(1/x + sqrt(1/x)sqrt(1+sqrt(x))) + sqrt(1/x - sqrt(1/x)sqrt(1+sqrt(x)))
2sqrt(1/x) sqrt(1 + sqrt(x))
= lim -----------------------------------------------------------------
sqrt(1/x)[sqrt(1+sqrt(x)sqrt(1+sqrt(x)))+sqrt(1-sqrt(x)sqrt(1+sqrt(x)))]
2
= ----------
2
= 1
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