How do you find the limit of 1/x [(1/(2+x) -1/2)]1x[(12+x−12)] as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Eddie Jul 3, 2016 = - 1/4=−14 Explanation: lim_{x to 0} 1/x (1/(2+x) -1/2) lim_{x to 0} 1/x ((2 - 2 - x)/(2(2+x)) ) lim_{x to 0} 1/x (( - x)/(2(2+x)) ) lim_{x to 0} ((-1)/(2(2+x)) ) = - 1/4 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 1166 views around the world You can reuse this answer Creative Commons License