Can δ-ε Definitions Prove This Infinite Limit Scenario?

Click For Summary
The discussion focuses on proving a limit scenario using the δ-ε definition of limits. The problem states that if the limit of g(x) as x approaches infinity is infinite and g(x) is less than or equal to f(x) as x approaches a, then the limit of f(x) as x approaches a must also be infinite. Participants express uncertainty about how to begin the proof and request guidance. Clarification is provided regarding the correct limit notation, emphasizing the need for accurate definitions in mathematical proofs. The conversation highlights the importance of starting with the formal definitions to establish the proof.
Jimbo57
Messages
96
Reaction score
0

Homework Statement



Prove, using the formal definition of limits:

If lim (x->inf) g(x) = inf and g(x) leq f(x) for x->a, then lim (x->a) f(x)=inf.

leq = less than or equal to.

Homework Equations


The Attempt at a Solution



Honestly, I'm not even sure where to start on this one. Anyone bored enough to show how they would solve it?
 
Physics news on Phys.org
Start with the δ-ε definition of a limit.

Show some work so we can help you. That's a rule for this Forum.

BTW: Don't you mean lim (x → a) g(x) = ∞ , NOT lim (x → ∞) ?
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Real analysis: prove the limit exists
  • · Replies 13 ·
Replies
13
Views
4K
Finding Limits Using the Epsilon-Delta Method
  • · Replies 8 ·
Replies
8
Views
2K
Proving Limit Exists: x-2 of f(x)=2
  • · Replies 2 ·
Replies
2
Views
1K
Rational epsilon-delta limit proof questions
  • · Replies 9 ·
Replies
9
Views
4K
f(x) = 2x+1, proving that it is continuous when p = 1 with 𝛿 and ε
  • · Replies 7 ·
Replies
7
Views
1K
Reversed limit definition for monotonic functions
  • · Replies 3 ·
Replies
3
Views
2K
Prove limit comparison test for Integrals
  • · Replies 2 ·
Replies
2
Views
2K
Sup. and Lim. Sup. are Measurable Functions
  • · Replies 7 ·
Replies
7
Views
3K
Ε-δ proof: lim x->a f(x) = lim h->0 f(a + h)
  • · Replies 8 ·
Replies
8
Views
7K
Epsilon-delta definition of limits
  • · Replies 20 ·
Replies
20
Views
3K