How do you find the limit of ( x+sin 2x)/( 3x) as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Shwetank Mauria Jul 1, 2016 Lt_(x->0)(x+sin2x)/(3x)=1 Explanation: Lt_(x->0)(x+sin2x)/(3x) = Lt_(x->0)(x/(3x)+(sin2x)/(3x)) = Lt_(x->0)(1/3+(sin2x)/(2x)xx(2x)/(3x)) = Lt_(x->0)(1/3)+Lt_(x->0)(sin2x)/(2x)xxLt_(x->0)(2x)/(3x) = 1/3+Lt_(2x->0)(sin2x)/(2x)xx2/3 = 1/3+1xx2/3 = 1/3+2/3=1 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 2251 views around the world You can reuse this answer Creative Commons License