What is the limit of #(e^(−7x))cos x# as x approaches infinity? Calculus Limits Determining Limits Algebraically 1 Answer Euan S. Aug 3, 2016 #lim_(xrarroo)(e^(-7x)cosx) = 0# Explanation: #cosx# is bounded as #xrarroo# as it flips back and forth between #1 and -1# indefinitely. It is distinctly finite though. #lim_(xrarroo) e^(-7x) = lim_(xrarroo) 1/(e^(7x)) = 1/oo = 0# This means we have #0*lim_(xrarroo)cosx # As #cosx# is bounded it remains finite and final limit is 0. 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 8010 views around the world You can reuse this answer Creative Commons License