• Support PF! Buy your school textbooks, materials and every day products Here!

Epsilon Delta Proof

  • Thread starter freezer
  • Start date
  • #1
76
0

Homework Statement



lim 3 as x->6
lim -1 as x->2

Homework Equations



In the first weeks of a calculus class and doing these epsilon delta proofs.

As i am looking at two of the problems i have been assigned:

Lim 3 as x->6
Lim -1 as x->2



The Attempt at a Solution


considering both are horzontal lines, if i give some ε then there is no intersection with the function and thus no δ. ε must be > 0 so not sure how our proof statement will work:

Given ε>0, choose δ=ε. If 0<0<δ, then |0|<δ, then |3-3| = |0| < δ=ε thus |3-3|<ε whenever 0<|0|<δ. Therefore, by the definition of a limit, lim 3 = 3 as x->6
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,226
951

Homework Statement



lim 3 as x->6
lim -1 as x->2

Homework Equations



In the first weeks of a calculus class and doing these epsilon delta proofs.

As i am looking at two of the problems i have been assigned:

Lim 3 as x->6
Lim -1 as x->2

The Attempt at a Solution


considering both are horizontal lines, if i give some ε then there is no intersection with the function and thus no δ. ε must be > 0 so not sure how our proof statement will work:

Given ε>0, choose δ=ε. If 0<0<δ, then |0|<δ, then |3-3| = |0| < δ=ε thus |3-3|<ε whenever 0<|0|<δ. Therefore, by the definition of a limit, lim 3 = 3 as x->6
Hello freezer. Welcome to PF !

One comment first: For a constant function, you can pick anything for δ, often just choose δ = 1.

Now for your proof. What is the general ε - δ formulation for limx → a f(x) = L ?

For any ε > 0, there exists a δ such that for any x for which 0 < |x - a| < δ, then |f(x) - L| < ε .

You don't have any x the following statement of yours.
... If 0<0<δ, then |0|<δ, then |3-3| = |0| < δ ...​
 

Related Threads for: Epsilon Delta Proof

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
5
Views
587
Top