this-x-lnx-2-1-ln-2-x-find-the-range-of-the-function-

Question Number 12703 by @ANTARES_VY last updated on 29/Apr/17

this \oint (x) = \frac{{lnx}^{2}}{1 + \ln^{2} x} find the

range of the function .

Answered by mrW1 last updated on 29/Apr/17

t = \ln x

y = \frac{2 \ln x}{1 + \ln^{2} x} = \frac{2 t}{1 + t^{2}}

{y t}^{2} - 2 t + y = 0

D = {(- 2)}^{2} - 4 y^{2} = 4 (1 - y^{2}) ⩾ 0

1 - y^{2} ⩾ 0

y \in [- 1, 1]

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