Question

Part I) Prove that if f and g are continuous at a, then f+g is continuous...

Part I) Prove that if f and g are continuous at a, then f+g is continuous at a using the epsilon-δ definition.

Part II) Let a, L ∈ R. Prove that if a ≥ L− ε for all positive, then a ≥ L.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that if f(x) is a continuous function and f(x) is not zero then g(x) =...
Prove that if f(x) is a continuous function and f(x) is not zero then g(x) = 1/f(x) is a continuous function.   Use the epsilon-delta definition of continuity and please overexplain and check your work before answering.
Use the ε-δ-definition of continuity to show that if f, g : D → R are...
Use the ε-δ-definition of continuity to show that if f, g : D → R are continuous then h(x) := f(x)g(x) is continuous in D.
Use ε − δ definition to prove that the function f (x) = 2x/3x^2 - 2...
Use ε − δ definition to prove that the function f (x) = 2x/3x^2 - 2 is continuous at the point p = 1.
Let D ⊆ R, a ∈ D, let f, g : D −→ R be continuous...
Let D ⊆ R, a ∈ D, let f, g : D −→ R be continuous functions. If limx→a f(x) = f(a) and limx→a g(x) = g(a) with f(a) < g(a), then there exists δ > 0 such that x ∈ D, 0 < |x − a| < δ =⇒ f(x) < g(x).
We know that any continuous function f : [a, b] → R is uniformly continuous on...
We know that any continuous function f : [a, b] → R is uniformly continuous on the finite closed interval [a, b]. (i) What is the definition of f being uniformly continuous on its domain? (This definition is meaningful for functions f : J → R defined on any interval J ⊂ R.) (ii) Given a differentiable function f : R → R, prove that if the derivative f ′ is a bounded function on R, then f is uniformly...
Show that if f and g are uniformly continuous on some interval I then cf (for...
Show that if f and g are uniformly continuous on some interval I then cf (for all c ∈ R) and f − g are all uniformly continuous on I
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) -...
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) - g(b)) < 0. a) Show that sup{|f(x) - g(x)| : x ϵ [a, b]} is strictly positive and achieved (is a maximum).
Apply ε − δ definition to show that f (x) = 1/x^2 is continuous in (0,  ∞).
Apply ε − δ definition to show that f (x) = 1/x^2 is continuous in (0,  ∞).
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0...
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0 for every x ∈ [a,b]. 1) Show that either f(x) > 0 for every x ∈ [a,b] or f(x) < 0 for every x ∈ [a,b]. 2) Assume that f(x) > 0 for every x ∈ [a,b] and prove that there exists ε > 0 such that f(x) ≥ ε for all x ∈ [a,b].
Using only definition 4.3.1 (continuity), prove that f(x)=x2+3x+4 is continuous on R.
Using only definition 4.3.1 (continuity), prove that f(x)=x2+3x+4 is continuous on R.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT