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Asymptotic Behaviors of Various Functions

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1) Determine the order of the following expressions as ??0:
?(?(1-?) ), (4?)^2 ?, 1000?^(1?2), ln?(1+?), (1-cos??)/(1+cos?? ), ?^(3?2)/(1+sin?? ), ?^(3?2)/(1-cos?? ),
sech ^(-1) ?, exp?(tan?? ), ln[1+(ln?(1+2?))/(1-2?)], ln[1+(1+2?)/(?(1-2?))], ?_0^? exp?(-s^2)ds.

2) Arrange the following in descending order for ??0. Use l'Hôpital's rule if you are uncertain about the ratio of any pairs of terms.
?^(1/2), (?e)^?,e^(-1/?),?^(1/2) ln?, (?(ln?)^2.

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https://brainmass.com/math/basic-algebra/asymptotic-behaviors-various-functions-459125

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We determine and compare the asymptotic behaviors of various functions.

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