Finding Limits of F(x) as x Approaches 64 and 0

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SUMMARY

The discussion focuses on finding limits of two functions as x approaches specific values. The first function, F(x) = (sqrt(x)-8)/((x)^(1/3)-4), is evaluated as x approaches 64, while the second limit, lim x-->0 ((x+1)^(1/3)-1)/((x+1)^(1/4)-1), is analyzed as x approaches 0. Participants suggest changing variables to the lowest common denominator and factoring to simplify the expressions. Specifically, they recommend using y = x^(1/6) for the first limit and y = (x+1)^(1/12) for the second limit to facilitate the calculations.

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Redoctober
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I spent a lot thinking of this but can't fingure out how to find the limit as it approach x=64
Plz need help :)

F(x) = (sqrt(x)-8)/((x)^(1/3)-4)

find f(x) lim x->64

also this question -

lim x-->0 ((x+1)^(1/3)-1)/((x+1)^(1/4)-1)

Thanks in advance
 
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Change variables to the lowest common denominator and factor and cancel
(sqrt(x)-8)/((x)^(1/3)-4) ->(y3-23)/(y2-22)
where y=x^(1/6)
((x+1)^(1/3)-1)/((x+1)^(1/4)-1)=(y4-14)/(y3-13)
where y=(x+1)^(1/12)
 
Thanks :D ! I though bout this way but i didnt know wat to put y as
 

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