# Formal Definition of a Limit at a Point - Page 3

Questions

- In the limit #lim 5/sqrt(2-x)=oo# as #x->2^-#, how do you find #delta>0# such that whenever #2-delta<x<2#, #5/sqrt(2-x)>100#?
- How do you prove that the limit of #f(x) =2x-3# as x approaches 5 is 7 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 that the limit of #(x^2+3x)=-18# as x approaches -3 using the epsilon delta proof?
- How do you find the Limit of #abs(x-2)# as #x->-2# and then use the epsilon delta definition to prove that the limit is L?
- How do you prove that the limit of #sqrtx = 3# as x approaches 9 using the epsilon delta proof?
- How do you prove that the limit of #(x^3 - 3) = 5# as x approaches 2 using the epsilon delta proof?
- How do you prove that the limit of #5 - 2x= 1# as x approaches 2 using the epsilon delta proof?
- How do you prove that the limit # 3/sqrt(x-5) = ∞# as x approaches #5^+# using the formal definition of a limit?
- How do you prove limit of #root3(x)# as #x->0# using the precise definition of a limit?
- Is the following statement True or False: " f'(x) exists for all real numbers x and f'(x) is never 0, then f(1) can not be equal to f(5). "?
- How do you use the epsilon delta definition to prove that the limit of #(1+x)/(4+x)=1/2# as #x->2#?
- How do you prove limit of #14-5x=4# as #x->2# using the precise definition of a limit?
- How do you use the epsilon delta definition to prove that the limit of #x^3+6x^2=32# as #x->2#?
- How do you prove that the #lim_(x to -2)(x^2 -5) = -1# using the formal definition of a limit?
- How do you prove that the limit of #x^2 - 5x + 6 = 2# as x approaches 1 using the epsilon delta proof?
- In the limit #lim x^-2=oo# as #x->0#, how do you find #delta>0# such that whenever #0<absx<delta#, #x^-2>10,000#?
- How do you prove that the limit of #sqrt(x+7)=3 # as x approaches 2 using the epsilon delta proof?
- How do you prove that the limit of # (x²-9) / (x²+5x+6)=0 # as x approaches -3 using the epsilon delta proof?
- How do you prove that the limit # (x^2 - 4x + 5) = 1# as x approaches 2 using the formal definition of a limit?