Suppose f is integrable on (-π, π] and extended to R by making it periodic of period 2π. Show that f(x) dx= | f(x)dz where I is any interval in R of length 2π Hint: I is contained in two consecutive...

Question

Question

Suppose f is integrable on (-π, π] and extended to R by making it periodic of period 2π. Show that f(x) dx= | f(x)dz where I

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Add a comment

Answer 2

Similar Homework Help Questions

2. (a) Suppose that f is Lebesgue integrable on R. Find the following limit: n sin(x/n f(x) dz. (b) Find the value of the limit in the special case: linn onsin(x/n) n→oo/.oo X(X2 + 1) dx. 2....

2. (a) Suppose that f is Lebesgue integrable on R. Find the following limit: n sin(x/n f(x) dz. (b) Find the value of the limit in the special case: linn onsin(x/n) n→oo/.oo X(X2 + 1) dx. 2. (a) Suppose that f is Lebesgue integrable on R. Find the following limit: n sin(x/n f(x) dz. (b) Find the value of the limit in the special case: linn onsin(x/n) n→oo/.oo X(X2 + 1) dx.
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series o...

5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series of the function in part (a) 5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0
19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a...

19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a)1/n. In particular, calculate J-3r2dr by consid- ering a partition P which divides the interval [2, 3] into n parts in geometric progression at the points 2, 2h, 2h2,2h3,... ,2h"-1,2h" -3 19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a)1/n....

4. Assume f and |fl are both integrable on la, b], a < b, show f(x) dx sf( d. Hint: there are several approaches. One good way is to apply the triangle inequality of series TL T& a where a, E...

4. Assume f and |fl are both integrable on la, b], a < b, show f(x) dx sf( d. Hint: there are several approaches. One good way is to apply the triangle inequality of series TL T& a where a, E R, ail s on the Riemann sums. 4. Assume f and |fl are both integrable on la, b], a
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that t...

Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...

Suppose f is integrable on (-π, π] and extended to R by making it periodic of period 2π. Show that f(x) dx= | f(x)dz where I is any interval in R of length 2π Hint: I is contained in two consecutive...

Homework Answers

Add Answer to:
Suppose f is integrable on (-π, π] and extended to R by making it periodic of period 2π. Show that f(x) dx= | f(x)dz where I is any interval in R of length 2π Hint: I is contained in two consecutive...

Post as a guest

Earn Coins

2. (a) Suppose that f is Lebesgue integrable on R. Find the following limit: n sin(x/n f(x) dz. (b) Find the value of the limit in the special case: linn onsin(x/n) n→oo/.oo X(X2 + 1) dx. 2....

5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series o...

19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a...

4. Assume f and |fl are both integrable on la, b], a < b, show f(x) dx sf( d. Hint: there are several approaches. One good way is to apply the triangle inequality of series TL T& a where a, E...

Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that t...

Suppose f is integrable on (-π, π] and extended to R by making it periodic of period 2π. Show that f(x) dx= | f(x)dz where I is any interval in R of length 2π Hint: I is contained in two consecutive...

Homework Answers

Add Answer to: Suppose f is integrable on (-π, π] and extended to R by making it periodic of period 2π. Show that f(x) dx= | f(x)dz where I is any interval in R of length 2π Hint: I is contained in two consecutive...

Post as a guest

Earn Coins

2. (a) Suppose that f is Lebesgue integrable on R. Find the following limit: n sin(x/n f(x) dz. (b) Find the value of the limit in the special case: linn onsin(x/n) n→oo/.oo X(X2 + 1) dx. 2....

5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series o...

19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a...

4. Assume f and |fl are both integrable on la, b], a < b, show f(x) dx sf( d. Hint: there are several approaches. One good way is to apply the triangle inequality of series TL T& a where a, E...

Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that t...

Add Answer to:
Suppose f is integrable on (-π, π] and extended to R by making it periodic of period 2π. Show that f(x) dx= | f(x)dz where I is any interval in R of length 2π Hint: I is contained in two consecutive...