Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R...

Question

Question

Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R be continuous, and suppose that |f(x)| ≤ g(x) for all x ∈ U. Show that if $\int_{u}g$ exists, then so does $\int_{u}f$ .

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Please comment if you need any clarification.

If you find my answer useful please put thumbs up. Thank you.

Sol - Given that UCR is open (not necessarily loounded) and figur is continous Also Ifalls glit, vrto. Now Ilfonde < sifcal d

Add a comment

Answer 2

Similar Homework Help Questions

Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that...

Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that T is positive if and only if = (here 1 denotes the constant function [0, 1] → R, x → 1). We were unable to transcribe this imageWe were unable to transcribe this image
Suppose is a bounded function for which there exists a partition such that . Prove: is...

Suppose is a bounded function for which there exists a partition such that . Prove: is a constant function f : a, b] →R We were unable to transcribe this imageL(P, f,a) = U(P, f,a) We were unable to transcribe this image
Let a, b ∈ R with a < b. Let f : [a, b] → [a,...

Let a, b ∈ R with a < b. Let f : [a, b] → [a, b] be continuous. Then there exists at least one ∈ [a, b] such that . We were unable to transcribe this imagef(x0) = x0

Let ⊂ be a rectangle and let f be a function which is integrable on R....

Let ⊂ be a rectangle and let f be a function which is integrable on R. Prove that the graph of f, G(f) := {(x, f(x)) ∈ : x ∈ }, is a Jordan region and that it has volume 0 (as a subset of ). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let f,g be continuous functions on [a,b] with for all (a) show that there are such...

Let f,g be continuous functions on [a,b] with for all (a) show that there are such that (b) using (a) prove that there is a strictly between x1 and x2 such that f(x) 0 rE a, b a, 1 ( f(xgf(x) < g[x2}f{x)) We were unable to transcribe this imagef(r)g()da g(e) f(x)da f(x) 0 rE a, b a, 1 ( f(xgf(x)
Let E be the solid bounded by the planes , , , , . Set up...

Let E be the solid bounded by the planes , , , , . Set up all six orders of integration for the evaluation of as an iterated integral. We were unable to transcribe this imageWe were unable to transcribe this imagey=0 We were unable to transcribe this imageWe were unable to transcribe this imagef(x, y, 2)d

Let U be an open subset of R. Let f: U C Rn → Rm. (a) Prove that f is continuously differentiable if and only if for ea...

Let U be an open subset of R. Let f: U C Rn → Rm. (a) Prove that f is continuously differentiable if and only if for each a є U, for each E > 0, there exists δ > 0 such that for each x E U, if IIx-all < δ, then llDf(x)-Df(a) ll < ε. (b) Let m n. Prove that if f is continuously differentiable, a E U, and Df (a) is invertible, then there exists δ...
Let n, and let n be a reduced residue. Let r = odd(). Prove that if...

Let n, and let n be a reduced residue. Let r = odd(). Prove that if r = st for positive integers s and t, then old(t) = s. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
3. Let f, g : [a,b] → R be functions such that f is integrable, g is continuous, and g(x) >0 for ...

3. Let f, g : [a,b] → R be functions such that f is integrable, g is continuous, and g(x) >0 for all r E [a, b] Since both f,g are bounded, let K >0 be such that lf(z)| K and g(x) K for all x E [a3] (a) Let n > 0 be given. Prove that there is a partition P of [a, b such that U (P. f) _ L(P./) < η and Mi(P4)-mi(P4) < η for all...

*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U...

*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U and a submersion if Dof is surjective for allv in U. (a) Suppose that f:U-R" is an immersion. Prove that, for each v in U, we can find an open set V of U containing v, an open set W of R" containing f...

Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R...

Homework Answers

Add Answer to:
Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R...

Post as a guest

Earn Coins

Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that...

Suppose is a bounded function for which there exists a partition such that . Prove: is...

Let a, b ∈ R with a < b. Let f : [a, b] → [a,...

Let ⊂ be a rectangle and let f be a function which is integrable on R....

Let f,g be continuous functions on [a,b] with for all (a) show that there are such...

Let E be the solid bounded by the planes , , , , . Set up...

Let U be an open subset of R. Let f: U C Rn → Rm. (a) Prove that f is continuously differentiable if and only if for ea...

Let n, and let n be a reduced residue. Let r = odd(). Prove that if...

3. Let f, g : [a,b] → R be functions such that f is integrable, g is continuous, and g(x) >0 for ...

*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U...

Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R...

Homework Answers

Add Answer to: Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R...

Post as a guest

Earn Coins

Add Answer to:
Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R...