Let f. q, and h be the functions defined on R by if – 1 4, and h(r) = e-2. Consider the following boundary problem (G): u(r,0) = h(x), lim u(r,t) + h(x), ¤€ R, t > 0 (1) I E R = 0, (2) Hint:F(e)= Va , where F(f()) is the fourier transform of f(r). (1) The Fourier Transform of f is given by: a. 2, cos (w). b. , sin (w). c. , sin (#). d. None of the above (2) The Fourier cosine Transform of g is given by: 2 sin(w) + cos(w) – - cos(4w)). b. 유(금sin(4w) +음 cos(4u) --급 cos(w)). a. A sin(w) + cos(w) – - cos(4w). d. None of the above (3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the Fourier Transform to the first equation of (G), we obtain: C. a. Ut – wU = te. b. Ut + w²U = e" c. U – w²U = d. None of the above (4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain a. U(w,t) = e-[1+(w² – 1)e-w²j. b. U (w, t) = e+[1+ w°e¬w°t]. c. U(w,t) = „3=e+*-*. d. None of the above (5) The general solution of (G) is: 1 a. u(r, t) = V2 Lw² e 1 efwz | 1 b. u(x,t) = 11 + w°e¬w°«]dw. [1 + (w² – 1)e-w*t] dw. roo 1 с. и (т,t) — 2w²e d. None of the above
Let f. q, and h be the functions defined on R by if – 1 4, and h(r) = e-2. Consider the following boundary problem (G): u(r,0) = h(x), lim u(r,t) + h(x), ¤€ R, t > 0 (1) I E R = 0, (2) Hint:F(e)= Va , where F(f()) is the fourier transform of f(r). (1) The Fourier Transform of f is given by: a. 2, cos (w). b. , sin (w). c. , sin (#). d. None of the above (2) The Fourier cosine Transform of g is given by: 2 sin(w) + cos(w) – - cos(4w)). b. 유(금sin(4w) +음 cos(4u) --급 cos(w)). a. A sin(w) + cos(w) – - cos(4w). d. None of the above (3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the Fourier Transform to the first equation of (G), we obtain: C. a. Ut – wU = te. b. Ut + w²U = e" c. U – w²U = d. None of the above (4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain a. U(w,t) = e-[1+(w² – 1)e-w²j. b. U (w, t) = e+[1+ w°e¬w°t]. c. U(w,t) = „3=e+*-*. d. None of the above (5) The general solution of (G) is: 1 a. u(r, t) = V2 Lw² e 1 efwz | 1 b. u(x,t) = 11 + w°e¬w°«]dw. [1 + (w² – 1)e-w*t] dw. roo 1 с. и (т,t) — 2w²e d. None of the above
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Related questions
Question
part 2 fourier cosine
![Let f. q, and h be the functions defined on R by
if – 1<x< 0,
if 0<r<1,
| 4x,
g(r) = {4 - ,
if 0 < x < 1,
if 1<r < 4,
1+x,
f(x) = {1-x,
0,
otherwise ,
0,
if r > 4,
and h(r) = e-2. Consider the following boundary problem (G):
u(r,0) = h(x),
lim u(r,t)
+ h(x), ¤€ R, t > 0 (1)
I E R
= 0,
(2)
Hint:F(e)=
Va
, where F(f()) is the fourier transform of f(r).
(1) The Fourier Transform of f is given by:
a. 2, cos (w).
b. , sin (w).
c. , sin (#).
d. None of the above
(2) The Fourier cosine Transform of g is given by:
2 sin(w) + cos(w) – - cos(4w)).
b. 유(금sin(4w) +음 cos(4u) --급 cos(w)).
a.
A sin(w) + cos(w) – - cos(4w).
d. None of the above
(3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the
Fourier Transform to the first equation of (G), we obtain:
C.
a. Ut – wU = te.
b. Ut + w²U = e"
c. U – w²U =
d. None of the above
(4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain
a. U(w,t) = e-[1+(w² – 1)e-w²j.
b. U (w, t) = e+[1+ w°e¬w°t].
c. U(w,t) = „3=e+*-*.
d. None of the above
(5) The general solution of (G) is:
1
a. u(r, t) =
V2
Lw² e
1
efwz |
1
b. u(x,t) =
11 + w°e¬w°«]dw.
[1 + (w² – 1)e-w*t] dw.
roo
1
с. и (т,t) —
2w²e
d. None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dcaa84c-83af-4054-aa96-9fc9f674a13b%2F903b65b8-2a60-46a0-b8e7-3de05f6ad407%2Fy6w6ccp_processed.png&w=3840&q=75)
Transcribed Image Text:Let f. q, and h be the functions defined on R by
if – 1<x< 0,
if 0<r<1,
| 4x,
g(r) = {4 - ,
if 0 < x < 1,
if 1<r < 4,
1+x,
f(x) = {1-x,
0,
otherwise ,
0,
if r > 4,
and h(r) = e-2. Consider the following boundary problem (G):
u(r,0) = h(x),
lim u(r,t)
+ h(x), ¤€ R, t > 0 (1)
I E R
= 0,
(2)
Hint:F(e)=
Va
, where F(f()) is the fourier transform of f(r).
(1) The Fourier Transform of f is given by:
a. 2, cos (w).
b. , sin (w).
c. , sin (#).
d. None of the above
(2) The Fourier cosine Transform of g is given by:
2 sin(w) + cos(w) – - cos(4w)).
b. 유(금sin(4w) +음 cos(4u) --급 cos(w)).
a.
A sin(w) + cos(w) – - cos(4w).
d. None of the above
(3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the
Fourier Transform to the first equation of (G), we obtain:
C.
a. Ut – wU = te.
b. Ut + w²U = e"
c. U – w²U =
d. None of the above
(4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain
a. U(w,t) = e-[1+(w² – 1)e-w²j.
b. U (w, t) = e+[1+ w°e¬w°t].
c. U(w,t) = „3=e+*-*.
d. None of the above
(5) The general solution of (G) is:
1
a. u(r, t) =
V2
Lw² e
1
efwz |
1
b. u(x,t) =
11 + w°e¬w°«]dw.
[1 + (w² – 1)e-w*t] dw.
roo
1
с. и (т,t) —
2w²e
d. None of the above
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