How do you use the epsilon delta definition to prove that the limit of #x^3+6x^2=32# as #x->2#? Calculus Limits Formal Definition of a Limit at a Point 1 Answer Alberto P. Oct 26, 2016 #delta(epsilon)=min(1;epsilon/49)# Explanation: #abs(x^3+6x^2-32)=abs(x-2)(x+4)^2# #abs(x-2) < min(1;epsilon/49) rArr (x+4)^2<(2+1+4)^2=49# and #abs(x^3+6x^2-32) < epsilon/49 * 49 = epsilon# Answer link Related questions How do you use the epsilon delta definition of limit to prove that #lim_(x->5)(x-1)= 4# ? How do you use the epsilon delta definition of limit to prove that #lim_(x->1)(x+2)= 3# ? What is the formal definition of limit? How do you use the limit definition to prove a limit exists? What is the definition of limit in calculus? How do you find the limit using the epsilon delta definition? How do you use the epsilon delta definition to prove a limit exists? What is the epsilon delta definition of limit? How do you find values of δ that correspond to ε=0.1, ε=0.05, and ε=.01 when finding the limit... How do you prove that the limit of #3x+5=35# as x approaches 10 using the precise definition of a limit? See all questions in Formal Definition of a Limit at a Point Impact of this question 1747 views around the world You can reuse this answer Creative Commons License