#lim_(y->0)e(1+ye^(-y/4))^(4/y) =# ? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Jan 4, 2017 #e^5# Explanation: #(e^x+4x)^(1/x)=e(1+4xe^(-x))^(1/x)# now making #y = 4x# #lim_(y->0)e(1+ye^(-y/4))^(4/y) = e(lim_(y->0)(1+ye^(-y/4))^(1/y))^4=ecdot e^4= e^5# 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 1052 views around the world You can reuse this answer Creative Commons License