The following function exhibits both flat and steep regions over a relatively short x region:
Determine the value of the definite
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- The values of p and h which renders (makes) the following set of equations dynamically and statically decoupled are, respectively. k,+k2 5 p+4 x1 = 0, X2 7 h+1 + [7h+1 J+e 5 p+4 J+e h= -0.214 and p = -1.76 h = -0.143 and p= -0.8 h = -0.281 and p= -1.2 h = -0.081 and p = -0.536arrow_forwardUse the process of partial fractions to determine the inverse Laplace of the following functions: s²2s 4 F(s) = (s − 3)(s + 2)(s − 1) 1.arrow_forward3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0arrow_forward
- Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) f(x, y) = 9 sin(x) sin(y), −? < x < ?, −? < y < ? local maximum value(s) local minimum value(s) saddle point(s) (x, y) =arrow_forwardGiven the data below: Xo = 1 X1= 2 x2 = 4 Axo) = 2 Ax1) = 3 Ax2 : = 8 (i) Calculate the second-order interpolating polynomial using the method of the Newton's interpolating polynomial. (ii) Use the interpolating polynomial in (i) to calculate the approximated/interpolated functional value at x = 3, i.e., (3). (iii)Calculate the percentage relative error if the true value of f(3) is 4.8.arrow_forwardDISCUSSION Before posting to the discussion board, complete the following: The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0arrow_forwardLet f(x) = √√√x, g(x) = x + 8 and h(x) = . Compute the following function X (fh)(4)arrow_forwardQ3) Find the optimal solution by using graphical method:. Max Z = x1 + 2x2 Subject to : 2x1 + x2 < 100 X1 +x2 < 80 X1 < 40 X1, X2 2 0arrow_forward2. Solve the following ODE in space using finite difference method based on central differences with error O(h). Use a five node grid. 4u" - 25u0 (0)=0 (1)=2 Solve analytically and compare the solution values at the nodes.arrow_forwardVerify if the following functions are Linear or not. Support your conclusion with appropriate reason. a) F(x) = b) f(x) =rcos wtarrow_forward/Simulate to solve the following ordinary differential equation by using Simulink tool box and represent the output result. x(t)= sin(3t) = 3x(t) + 1-2y dtarrow_forwardPlease solve the following two problems:arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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