Question #27259 Calculus Limits Determining Limits Algebraically 2 Answers kubik98 Dec 20, 2017 e^(-4)e−4 Explanation: Lim_(xrarroo)((3x-4)/(3x+2))^(2x-4) Lim_(xrarroo)((3x+2-6)/(3x+2))^(2x-4) Lim_(xrarroo)((3x+2)/(3x+2)+(-6)/(3x+2))^(2x-4) Lim_(xrarroo)(1+1/((3x+2)/(-6)))^(2x-4) Lim_(xrarroo)(1+1/((3x+2)/(-6)))^((2x-4)(3x+2)/(-6)*(-6)/(3x+2)) Lim_(xrarroo)[(1+1/((3x+2)/(-6)))^((3x+2)/(-6))]^((2x-4)*(-6)/(3x+2)) Lim_(xrarroo)(1+1/x)^x=e e^(Lim_(xrarroo)((-12x+24)/(3x+2))) e^(-12/3)=e^(-4) Answer link Cesareo R. Dec 20, 2017 e^-4 Explanation: Making 1+1/y = ((3 x - 4)/(3 x + 2)) or equivalently x = -2/3(3y+1) we have ((3 x - 4)/(3 x + 2))^(2 x - 4) equiv (1+1/y)^(-(4y+16/3))=1/( (1+1/y)^(4y+16/3)) and then lim_(x->oo)((3 x - 4)/(3 x + 2))^(2 x - 4) =1/( lim_(y->oo)(1+1/y)^(4y+16/3)) = 1/e^4 = e^-4 Answer link Related questions How do you find the limit lim_(x->5)(x^2-6x+5)/(x^2-25) ? How do you find the limit lim_(x->3^+)|3-x|/(x^2-2x-3) ? How do you find the limit lim_(x->4)(x^3-64)/(x^2-8x+16) ? How do you find the limit lim_(x->2)(x^2+x-6)/(x-2) ? How do you find the limit lim_(x->-4)(x^2+5x+4)/(x^2+3x-4) ? How do you find the limit lim_(t->-3)(t^2-9)/(2t^2+7t+3) ? How do you find the limit lim_(h->0)((4+h)^2-16)/h ? How do you find the limit lim_(h->0)((2+h)^3-8)/h ? How do you find the limit lim_(x->9)(9-x)/(3-sqrt(x)) ? How do you find the limit lim_(h->0)(sqrt(1+h)-1)/h ? See all questions in Determining Limits Algebraically Impact of this question 1652 views around the world You can reuse this answer Creative Commons License