To determine The value of L ( f 1 ) where f 1 ( t ) = 0 if t ≤ 2 and f 2 ( t ) = 1 if t > 2 . Explanation Property used: Linearity property: The transform of a sum of functions is the sum of the transforms and is written as L [ a f ( t ) + b g ( t ) ] = a L ( f ) + b L ( g ) Calculation: From Problem 10, the function is as follows: f ( t ) = { k 0 < t < c 0 t ≥ c Also, the Laplace transform of the above function is k s ( 1 − e − c s ) . The function f 1 can be written as, f 1 ( t ) = { 0 t ≤ 2 1 t > 2 Substitute c = 2 , k = 1 in f ( t ) as, f ( t ) = { 1 0 < t < 2 0 t ≥ 2 Thus, f 1 ( t ) + f ( t ) = 1 for t ≤ 2 and t ≥ 2 . That is, for all t . Substitute c = 2 , k = 1 in L ( f ) = k s ( 1 − e − c s ) as, L ( f ) = 1 s ( 1 − e − 2 s ) Use linearity property and simplify L [ f 1 ( t ) + f ( t ) ] = L [ 1 ]

10th Edition

ISBN: 9781119096023

Author: Kreyszig

Publisher: WILEY

See similar textbooks

Videos

Question

Chapter 6.1, Problem 18P

To determine

The value of L(f1) where f1(t)=0 if t≤2 and f2(t)=1 if t>2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.1, Problem 17P

Chapter 6.1, Problem 19P

Students have asked these similar questions

5) State any theorems that you use in determining your solution. a) Suppose you are given a model with two explanatory variables such that: Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n Using partial differentiation derive expressions for the intercept and slope coefficients for the model above. [25 marks] b) A production function is specified as: Yi = α + B₁x1i + ẞ2x2i + Ui, i = 1, 2, ... n, u₁~N(0,σ²) where: y = log(output), x₁ = log(labor input), x2 = log(capital input) The results are as follows: x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10, = 8, Syy = 10, S2y n = 23 (individual firms) i) Compute values for the intercept, the slope coefficients and σ². [20 marks] ii) Show that SE (B₁) = 0.102. [15 marks] iii) Test the hypotheses: ẞ1 = 1 and B2 = 0, separately at the 5% significance level. You may take without calculation that SE (a) = 0.78 and SE (B2) = 0.102 [20 marks] iv) Find a 95% confidence interval for the estimate ẞ2. [20 marks]

Page < 2 of 2 - ZOOM + The set of all 3 x 3 upper triangular matrices 6) Determine whether each of the following sets, together with the standard operations, is a vector space. If it is, then simply write 'Vector space'. You do not have to prove all ten vector space axioms. If it is not, then identify one of the ten vector space axioms with its number in the attached sheet that fails and also show that how it fails. a) The set of all polynomials of degree four or less. b) The set of all 2 x 2 singular matrices. c) The set {(x, y) : x ≥ 0, y is a real number}. d) C[0,1], the set of all continuous functions defined on the interval [0,1]. 7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and show that it is orthogonal to both u and v. 8) a) Find the equation of the least squares regression line for the data points below. (-2,0), (0,2), (2,2) b) Graph the points and the line that you found from a) on the same Cartesian coordinate plane.

Page < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.

Chapter 6 Solutions

ADVANCED ENGINEERING MATH W/ACCESS

Knowledge Booster

$Advanced Math$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

The value of L ( f 1 ) where f 1 ( t ) = 0 if t ≤ 2 and f 2 ( t ) = 1 if t &gt; 2 .

Videos

The value of L(f1) where f1(t)=0 if t≤2 and f2(t)=1 if t>2.

Want to see the full answer?

Chapter 6 Solutions

The value of L ( f 1 ) where f 1 ( t ) = 0 if t ≤ 2 and f 2 ( t ) = 1 if t > 2 .