barcode in ssrs report s2 lfY x g sY 0 Y 0 0 lfY x g 1=s2 in .NET framework

Generator Quick Response Code in .NET framework s2 lfY x g sY 0 Y 0 0 lfY x g 1=s2

s2 lfY x g sY 0 Y 0 0 lfY x g 1=s2
Reading QR Code JIS X 0510 In Visual Studio .NET
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET applications.
Making QR In .NET Framework
Using Barcode creation for .NET Control to generate, create QR-Code image in Visual Studio .NET applications.
Solving for lfY x g using the given conditions, we nd lfY x g by methods of partial fractions. Since 1 1 1 1 lfxg and 2 lfsin xg; it follows that 2 2 lfx sin xg: s2 s 1 s s 1 s2 s2 2s2 1 1 1 s2 s2 1 1
Quick Response Code Recognizer In VS .NET
Using Barcode decoder for .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Painting Barcode In Visual Studio .NET
Using Barcode generator for .NET Control to generate, create bar code image in .NET framework applications.
Hence, from (1), lfY x g lfx sin xg, from which we can conclude that Y x x sin x which is, in fact, found to be a solution. Another method: If lfF x g f s , we call f s the inverse Laplace transform of F x and write f s l 1 fF x g. By Problem 12.78, l 1 f f s g s g l 1 f f s g l 1 fg s g. Then from (1), & ' & ' & ' 1 1 1 1 l 1 2 l 1 2 x sin x Y x l 1 2 2 s s 1 s s 1 Inverse Laplace transforms can be read from the table on Page 315.
Read Bar Code In VS .NET
Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
Encode QR In C#
Using Barcode maker for .NET framework Control to generate, create QR-Code image in .NET framework applications.
Supplementary Problems
Creating QR Code In .NET
Using Barcode encoder for ASP.NET Control to generate, create Denso QR Bar Code image in ASP.NET applications.
Create QR In VB.NET
Using Barcode maker for .NET framework Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications.
IMPROPER INTEGRALS OF THE FIRST KIND 12.37. Test for convergence: 1 2 x 1 dx a 4 0 x 1 1 b
EAN13 Encoder In .NET Framework
Using Barcode drawer for .NET framework Control to generate, create EAN-13 image in .NET framework applications.
Painting UPC Code In .NET
Using Barcode creator for VS .NET Control to generate, create UPC Symbol image in .NET framework applications.
1 d
Print 1D Barcode In Visual Studio .NET
Using Barcode generator for .NET Control to generate, create 1D Barcode image in .NET framework applications.
Code 2 Of 7 Creator In Visual Studio .NET
Using Barcode generation for VS .NET Control to generate, create Code-27 image in .NET framework applications.
dx 4
EAN 13 Printer In Visual Basic .NET
Using Barcode creation for .NET framework Control to generate, create EAN-13 Supplement 5 image in VS .NET applications.
Encode DataMatrix In None
Using Barcode generator for Font Control to generate, create Data Matrix image in Font applications.
1 g
Read Bar Code In Java
Using Barcode Control SDK for BIRT Control to generate, create, read, scan barcode image in Eclipse BIRT applications.
Decode EAN13 In None
Using Barcode reader for Software Control to read, scan read, scan image in Software applications.
x2 dx 5=2 1 x x 1
Scan ANSI/AIM Code 128 In None
Using Barcode decoder for Software Control to read, scan read, scan image in Software applications.
Making UCC-128 In None
Using Barcode maker for Software Control to generate, create EAN128 image in Software applications.
x dx p x3 1 dx p x 3x 2
Code 128 Maker In Java
Using Barcode generation for Java Control to generate, create ANSI/AIM Code 128 image in Java applications.
Generate UPC Symbol In None
Using Barcode maker for Software Control to generate, create GS1 - 12 image in Software applications.
1 e
2 sin x dx 2 1 x 1 x dx ln x 3
1 h
ln x dx x e x sin2 x dx x2
1 c
1 f
1 i
Ans. (a) conv., (b) div., (c) conv., (d) conv., (e) conv., ( f ) div., (g) conv., (h) div., (i) conv. 1 12.38. Prove that
dx  p if b > jaj. 2 a2 x2 2ax b2 b 1 1 1 b
12.39. Test for convergence: Ans. (a) conv.,
e x ln x dx; (c) div.
e x ln 1 ex dx;
1 c
e x cosh x2 dx.
(b) conv.,
CHAP. 12]
IMPROPER INTEGRALS 1
sin 2x dx; x3 1
12.40. Test for convergence, indicating absolute or conditional convergence where possible: 1 (b) 1 (e)
0 1
(a) 1
e ax cos bx dx, where a; b are positive constants; cos x dx. cosh x
1 (c)
cos x p dx; x2 1
x sin x p dx; x2 a2
Ans.
(a) abs. conv.,
(b) abs. conv.,
(c) cond. conv.,
(d) div.,
(e) abs. conv.
12.41. Prove the quotient tests (b) and (c) on Page 309. IMPROPER INTEGRALS OF THE SECOND KIND 12.42. Test for convergence: 1 dx p a 2 0 x 1 1 x b 1 cos x dx 2 0 x
ln x p dx 3 8 x3 1
x2 dx 2 0 3 x e x cos x dx x
j
dx x 0 x
dx p ln 1=x 0
=2
etan x 1
=2 ln sin x dx
s 1 k2 x 2 dx; jkj < 1 1 x2 0
Ans. (a) conv., (b) div., ( j conv. 5 12.43. (a) Prove that
(c) div., (d) conv., (e) conv., ( f conv., (g) div., (h) div., (i) conv.,
dx diverges in the usual sense but converges in the Cauchy principal value senses. 4 x 0 (b) Find the Cauchy principal value of the integral in (a) and give a geometric interpretation. Ans. (b) ln 4
12.44. Test for convergence, indicating absolute or conditional convergence where possible:       1 1 1 1 1 1 1 1 cos a cos cos dx; b dx; c dx: 2 x x x 0 0x 0x Ans. (a) abs. conv., 4  12.45. Prove that
(b) cond. conv.,
(c) div.
p  1 1 32 2 dx 3x2 sin x cos . x x 3 1 c
IMPROPER INTEGRALS OF THE THIRD KIND 1 1 e x dx p ; e x ln x dx; b 12.46. Test for convergence: (a) x ln x 1 0 0 Ans. (a) conv., (b) div., (a)
e x dx p . 3 x 3 2 sin x
(c) conv. 1 dx p ; 3 x4 x2 1 b
12.47. Test for convergence: Ans.
ex dx p ; a > 0. sinh ax
(a) conv., (b) conv. if a > 2, div. if 0 < a @ 2. 1 sinh ax dx converges if 0 @ jaj <  and diverges if jaj @ . sinh x
12.48. Prove that
12.49. Test for convergence, indicating absolute or conditional convergence where possible:
1 a
IMPROPER INTEGRALS 1 b
[CHAP. 12
sin x p dx; x
p sin x p dx: sinh x
Ans:
a cond. conv.,
b abs. conv.
UNIFORM CONVERGENCE OF IMPROPER INTEGRALS 1 cos x dx is uniformly convergent for all . 12.50. (a) Prove that  2 0 1 x Ans. (c) =2: (b) Prove that  is continuous for all . (c) Find lim  : !0 1 2 12.51. Let  F x; dx, where F x; 2 xe x . (a) Show that  is not continuous at 0, i.e., 0 1 1 F x; dx 6 lim F x; dx. (b) Explain the result in (a). lim
!0 0 0 !0
12.52. Work Problem 12.51 if F x; 2 xe x . 12.53. If F x is bounded and continuous for 1 < x < 1 and 1 1 yF  d V x; y  1 y2  x 2 prove that lim V x; y F x .
12.54. Prove (a) Theorem 7 and (b) Theorem 8 on Page 314. 12.55. Prove the Weierstrass M test for uniform convergence of integrals. 1 1 F x dx converges, then e x F x dx converges uniformly for A 0. 12.56. Prove that if 0 0 1 sin x  dx converges uniformly for a A 0, b  a tan 1 a, e ax 12.57. Prove that a  a x 2 0 1 sin x  dx (compare Problems 12.27 through 12.29). (c) x 2 0 12.58. State the de nition of uniform convergence for improper integrals of the second kind. 12.59. State and prove a theorem corresponding to Theorem 8, Page 314, if a is a di erentiable function of . EVALUATION OF DEFINITE INTEGRALS Establish each of the following results. Justify all steps in each case. 1 ax e e bx dx ln b=a ; a; b > 0 12.60. x 0 1 12.61.
e ax e bx dx tan 1 b=r tan 1 a=r ; x csc rx sin rx  dx 1 e r ; 2 x 1 x2 1 cos rx  dx jrj 2 x2 x sin rx  dx e ar ; 2 a2 x2 a; r A 0 rA0
Copyright © OnBarcode.com . All rights reserved.