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Consider the following initial-value problem. 5 f'(x) f(1) = 17 Integrate the function f'(x). (Use C...
Use integration by parts to derive the following formula. ſxIn \/ dx=x** 12+Cnt=1 (n+1) If u...
Use integration by parts to derive the following formula. ſxIn \/ dx=x** 12+Cnt=1 (n+1) If u and v are differentiable functions, then udv=uv - vdu. Let udv = x. In|x dx. Determine the best expressions for u and dv. Select the correct answer below and fill in the answer boxes to complete your answer. O A. u= O B. u= dx, dv= dv= dx Find du du= dx Integrate dv to find v. The constant of integration is not introduced...
Consider the following initial value problem: dy = sin(x - y) dx, y(0) 1. Write the...
Consider the following initial value problem: dy = sin(x - y) dx, y(0) 1. Write the equation in the form ay = G(ax +by+c), dx where a, b, and c are constants and G is a function. 2. Use the substitution u = ax + by + c to transfer the equation into the variables u and x only. 3. Solve the equation in (2). 4. Re-substitute u = ax + by + c to write your solution in terms...
Consider the initial value problem for function y given by, Consider the initial value problem for...
Consider the initial value problem for function y given by,
Consider the initial value problem for function y given by, (a) Find the Laplace Transform of the source function, F(s) = L[-3 F(s) = (b) Find the Laplace Transform of the solution, Y(s) Lt) Y(s) - (c) Find the solution y(t) of the initial value problem above. s(t) Recall: If needed, the step function at c is denoted as u(t - c) -1] Help Entering Answers Preview My Anawers Submit...
Find f(x), assuming that f(x) ex dx = f(x) e' - 8x-1 ex dx. (Use C...
Find f(x), assuming that f(x) ex dx = f(x) e' - 8x-1 ex dx. (Use C for the constant of integration.) Evaluate the integral. (Use C for the constant of integration.) cos 498(3y) sin?(3y) dy
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Use Matlab code Consider the following function sin(x) Using the following parameters in your functions: -func:...
Use
Matlab code
Consider the following function sin(x) Using the following parameters in your functions: -func: the function/equation that you are required to integrate -a, b: the integration limits n: the number of points to be used for the integration I:Integral estimate a) Write a function capable of performing numerical integration of h(x) using the composite trapezoidal rule. Use your function to integration the equation with 9 points. Write a function capable of performing numerical integration of h(x) using the...
17. Consider the differential equation given by dy/dx = xy/2
17. Consider the differential equation given by dy/dx = xy/2 (A) On the axes provided, sketch a slope field for the given differential equation. (B) Let f be the function that satisfies the given differential equation. Write an equation for the tangent line to the curve y (x) through the point (1, 1). Then use your tangent line equation to estimate the value of f(1.2) (C) Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution...
Find f by solving the initial value problem. 6 f'(x) = Ponce f(9) = 37 Find...
Find f by solving the initial value problem. 6 f'(x) = Ponce f(9) = 37 Find f(x) by solving the initial value problem. f'(x) = 3er - 10x; f(0) = 10 f(x) =
in matlab -Consider the equation f(x) = x-2-sin x = 0 on the interval x E [0.1,4 π] Use a plot to approximately locate the roots of f. To which roots do the fol- owing initial guesses converge wh...
in
matlab
-Consider the equation f(x) = x-2-sin x = 0 on the interval x E [0.1,4 π] Use a plot to approximately locate the roots of f. To which roots do the fol- owing initial guesses converge when using Function 4.3.1? Is the root obtained the one that is closest to that guess? )xo = 1.5, (b) x0 = 2, (c) x.-3.2, (d) xo = 4, (e) xo = 5, (f) xo = 27. Function 4.3.1 (newton) Newton's method...
11. The graph of fis shown. Determine the value of f (x)dx= y = f(x) -...
11. The graph of fis shown. Determine the value of f (x)dx= y = f(x) - X 16 32 48 64 1 12. Consider the definite integral s sin(tw) dw. What is the interval of integration for this integral? What is the variable of integration? What is the integrand? 13. Suppose that f* f(x) dx = 5, ſ. f(x)dx = -3, * g(x)dx = -1 and 1 g(x)dx = 7. Determine the value of each integral. Box Answer (5) $(x)+...
Use integration by parts to derive the following formula. ſxIn \/ dx=x** 12+Cnt=1 (n+1) If u and v are differentiable functions, then udv=uv - vdu. Let udv = x. In|x dx. Determine the best expressions for u and dv. Select the correct answer below and fill in the answer boxes to complete your answer. O A. u= O B. u= dx, dv= dv= dx Find du du= dx Integrate dv to find v. The constant of integration is not introduced...
Consider the following initial value problem: dy = sin(x - y) dx, y(0) 1. Write the equation in the form ay = G(ax +by+c), dx where a, b, and c are constants and G is a function. 2. Use the substitution u = ax + by + c to transfer the equation into the variables u and x only. 3. Solve the equation in (2). 4. Re-substitute u = ax + by + c to write your solution in terms...
Consider the initial value problem for function y given by,
Consider the initial value problem for function y given by, (a) Find the Laplace Transform of the source function, F(s) = L[-3 F(s) = (b) Find the Laplace Transform of the solution, Y(s) Lt) Y(s) - (c) Find the solution y(t) of the initial value problem above. s(t) Recall: If needed, the step function at c is denoted as u(t - c) -1] Help Entering Answers Preview My Anawers Submit...
Find f(x), assuming that f(x) ex dx = f(x) e' - 8x-1 ex dx. (Use C for the constant of integration.) Evaluate the integral. (Use C for the constant of integration.) cos 498(3y) sin?(3y) dy
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Use
Matlab code
Consider the following function sin(x) Using the following parameters in your functions: -func: the function/equation that you are required to integrate -a, b: the integration limits n: the number of points to be used for the integration I:Integral estimate a) Write a function capable of performing numerical integration of h(x) using the composite trapezoidal rule. Use your function to integration the equation with 9 points. Write a function capable of performing numerical integration of h(x) using the...
Find f by solving the initial value problem. 6 f'(x) = Ponce f(9) = 37 Find f(x) by solving the initial value problem. f'(x) = 3er - 10x; f(0) = 10 f(x) =
in
matlab
-Consider the equation f(x) = x-2-sin x = 0 on the interval x E [0.1,4 π] Use a plot to approximately locate the roots of f. To which roots do the fol- owing initial guesses converge when using Function 4.3.1? Is the root obtained the one that is closest to that guess? )xo = 1.5, (b) x0 = 2, (c) x.-3.2, (d) xo = 4, (e) xo = 5, (f) xo = 27. Function 4.3.1 (newton) Newton's method...
11. The graph of fis shown. Determine the value of f (x)dx= y = f(x) - X 16 32 48 64 1 12. Consider the definite integral s sin(tw) dw. What is the interval of integration for this integral? What is the variable of integration? What is the integrand? 13. Suppose that f* f(x) dx = 5, ſ. f(x)dx = -3, * g(x)dx = -1 and 1 g(x)dx = 7. Determine the value of each integral. Box Answer (5) $(x)+...
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