Question

Use the pinching theorem for limits to show that if f, g and h are three...

Use the pinching theorem for limits to show that if f, g and h are three functions defined on an open interval I, such that
• f(x) ≤ g(x) ≤ h(x) for all x ∈ I,

• f(a) = g(a) = h(a) for some a ∈ I, and

• f and h are continuous at a,

then g is also continuous at a.

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
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 : X −→ C denote continuous functions from the open subset X of...
Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following: (a) The sum f+g is a continuous function. (b) The product fg is a continuous function. (c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.
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.
1. Let f : R2 → R2, f(x,y) = ?g(x,y),h(x,y)? where g,h : R2 → R....
1. Let f : R2 → R2, f(x,y) = ?g(x,y),h(x,y)? where g,h : R2 → R. Show that f is continuous at p0 ⇐⇒ both g,h are continuous at p0
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select...
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = cos x,    [π, 3π] Yes. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). No, because f(a) ≠ f(b). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = 0. (Enter your answers...
please show all the step to simplify this by taylor theorem 1/12h | f(x-2h)-8f(x-h)+8f(x+h)-f(x+2h) |
please show all the step to simplify this by taylor theorem 1/12h | f(x-2h)-8f(x-h)+8f(x+h)-f(x+2h) |
Determine whether the Mean Value theorem can be applied to f on the closed interval [a,...
Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 8 − x ,    [−17, 8] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open...
Let⇀H=〈−y(2 +x), x, yz〉 (a) Show that ⇀∇·⇀H= 0. (b) Since⇀H is defined and its component...
Let⇀H=〈−y(2 +x), x, yz〉 (a) Show that ⇀∇·⇀H= 0. (b) Since⇀H is defined and its component functions have continuous partials on R3, one can prove that there exists a vector field ⇀F such that ⇀∇×⇀F=⇀H. Show that F = (1/3xz−1/4y^2z)ˆı+(1/2xyz+2/3yz)ˆ−(1/3x^2+2/3y^2+1/4xy^2)ˆk satisfies this property. (c) Let⇀G=〈xz, xyz,−y^2〉. Show that⇀∇×⇀G is also equal to⇀H. (d) Find a function f such that⇀G=⇀F+⇀∇f.
Show that, if g : Y → X and h : Y → X are both...
Show that, if g : Y → X and h : Y → X are both inverses to f, then g = h (two functions are equal if their domains are the same, D(g) = D(h) = D and g(y) = h(y) ∀y ∈ D).
Determine whether the Mean Value theorem can be applied to f on the closed interval [a,...
Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f (x) = x7, [0,1] Yes, the Mean Value Theorem can be applied. No, f is not continuous on [a, b]. No, f is not differentiable on (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f ‘(c) = f (b)...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT