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I have to find these limits WITHOUT using the Hpital's rule (lim x->c f(x)/g(x) = lim x->c f'(x)/g'(x)), but I'm having trouble doing so. #1

I have to find these limits WITHOUT using the Hpital's rule (lim x->c f(x)/g(x) = lim x->c f'(x)/g'(x)), but I'm having trouble doing so.

#1 : lim x->+infinity. ((3x+1)/(3x-1))^3x

#2 : lim x->+infinity. ln(1+(1/(2x+1)))^2x

#3 : lim x->-infinity. (x-1)(ln(2-x)-ln(1-x))

#4 : lim x->+infinity. sinx/(x^2)

#5 : lim x->(pi/5). (sinx-sin(pi/5))/(x-(pi/5))

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