(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x) = sqroot(ax^2 + 1 ) - x

find all the different limits in + infinity that f can have with all the different "a" values

2. Relevant equations

3. The attempt at a solution

i dont know if i did something wrong here :

- if a = 0 then f = 1 - x, limit : - infinty

- if a < 0 then no f value in + infinite

, (except if a = ' - 1 / +infnte', limit : - infinte)

- if a > 0 then

lim infinite ( f(x) ) = lim +infinite ( root (ax^2 . (1 + 1 / ax^2) ) - x )

= lim +infinte ( root(a) . x - x)

= lim +infinte ( (root(a) - 1) x)

so if a = 1, limit is 0

if a > 1 , limit is + infinity

if 0 < a < 1, limit is - infinity

PS ; if badly wrote, ect, im sorry , but i was on a pc with a wierd keyboard that really thrustrated me

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# Homework Help: Find all the different limits in + infinity

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