# Formal Definition of a Limit at a Point - Page 4

Questions

- How do you use the formal definition of a limit to prove #lim (x^2-x+1)=1# as x approaches 1?
- How do you prove that the limit of #x^(3) = -8# as x approaches -2 using the epsilon delta proof?
- Is the statement "if limit of f(x)=L as x approaches c, then f(c)=L" a true or false statement?
- The graphs of the triad #y = cosh x, y = sinh x and y = e^x# meet x = 1 at (1, cosh 1), (1, sinh 1) and (1, e). How do you find these points for the FCF-triad #y=cosh(x(1+1/y)), y=sinh(x(1+1/y)) and y=e^(x(1+1/y))#?
- How do you find values of δ that correspond to ε=0.1, ε=0.05, and ε=.01 when finding the limit of #(5x-7)# as x approaches 2?
- How do you use the epsilon delta definition to prove that the limit of #x^3=27# as #x->3#?
- How do you use the epsilon delta definition of limit to prove that #lim_(x->1)(x+2)= 3# ?
- How do you prove that the limit of #(x^2 - 4x + 5) = 1# as x approaches 2 using the epsilon delta proof?
- How do you prove that the limit of #x-2 = 2# as x approaches 3 using the epsilon delta proof?
- How do you prove that the limit of #f(x) = 2 - (1/x)# as x approaches 1 using the epsilon delta proof?
- How do you use the epsilon delta definition to prove that the limit of #x/(6-x)=1# as #x->3#?
- How do you prove that the limit #x^(1/2) = 4# as x approaches 16 using the formal definition of a limit?
- How do you prove that the limit of #x+2y= 1# as (x,y) approaches (1,0) using the epsilon delta proof?
- How do you prove that the limit of #x^2 = 9# as x approaches 3 using the epsilon delta proof?
- How do you prove limit of #x^2-3x=-2# as #x->2# using the precise definition of a limit?
- In the limit #lim 16/x^4=oo# as #x->0#, how do you find #delta>0# such that whenever #0<absx<delta#, #16/x^4>10,000#?
- How do you find the Limit of #-1# as #x->2# and then use the epsilon delta definition to prove that the limit is L?
- How do you prove that the #lim_(xrarr3) (4x-5)=7# using the formal definition of a limit?
- How do you use the formal definition of a limit to prove #lim(x^3 + 3x + 5) = 19# as x approaches 2?
- How do you use the epsilon delta definition to prove that the limit of #sqrt(x+6)=9# as #x->3#?