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## Homework Statement

http://img227.imageshack.us/img227/9792/hopitalsruleandlimits.png [Broken]

Ive added a picture of the question. I know that L'hopitals rule is lim x->a f(x)/g(x) = lim x->a f'(x)/g'(x) but I dont understand how to apply it in this situation >< and the other questions I dont understand how to start off and what to get to. If anyone could please help me with ANY of the questions i would be so grateful!

## Homework Equations

## The Attempt at a Solution

progress so far

a) I don't know how get it from positive and from the negative side using the rule, but I used values and from below 1/2 and it approaches 0 from the positive and from above 1/2 it approaches 0

b) i) I've shown its an even function using x= 1 and x= -1

ii) uses stuff from a) so I dont know how to do it. but i assume it does has a limit.. i dont know an explanation though

iii) wild guess.. limit at -1/2 and 1/2 should be.. 0? but why? (if it does = 0)

c) i) I know how to find the derivative using the product rule but I dont understand why its x > 1/2 and -1/2 < x < 1/2

ii) similar to a) dont know how to do that

iii) dont know

iv) f'(3/4) i subbed in the value to upper derivative from above and i get to log [ (5/4)

^{1/4}/ 4

^{5/4}] and im not sure how to go from there

f'(5/6) = log [ (4/3)

^{1/3}/ 3

^{4/3}how can i simplify that..?

and i dont know what the second part of the question means

v) dont know

d) any easy way of finding f"(x)? or do i have to find the equ using quotient rule and not sure what the explanation should be

e) same with a), not sure how to calculate from infinity from +side and -side.. sub values?

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