Formal Definition of a Limit at a Point - Page 6

Questions
  • How do you prove that the limit of #1/(x-3)# does not exist as x approaches 3 using the epsilon delta proof?
  • How do you use the epsilon delta definition of limit to prove that #lim_(x->5)(x-1)= 4# ?
  • How do you prove that the limit #(x^2 - 1) = 3# as x approaches -2 using the formal definition of a limit?
  • How do you prove that the limit of #(x^2 - x) = 0 # as x approaches 1 using the epsilon delta proof?
  • In the limit #lim 1/(10t)=oo# as #t->0^+#, how do you find #delta>0# such that whenever #0<t<delta#, #1/(10t)>100#?
  • How do you find the Limit of #2x+5# as #x->-3# and then use the epsilon delta definition to prove that the limit is L?
  • What is limit of |x| as it approach zero?
  • Find the following limits if they exist. #lim_(x->5)(|10-2x|)/(3x^2-13x-10)#? #lim_(x->1)(sqrtx-1)/(root(3)x -1)#? Please help