Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find t...
(Bernoulli Equations) Let p, f : I → R be continous functions defined on an interval I of R. Then for every α є R\ {0, 1), the 1st-order differential equation is called Bernoulli equation. It is a nonlinear ordinary differential equation. (a) Use the literature and describe in brief steps a method to find a solution of equation (1) Hint: See Trench, p.63 (b) Find all solutions to the following two differential equations. Use Mathematica to plot a direction...
Please help! 1. (Bernoulli Equations) Let p, f : I → R be continous functions defined on an interval I of R. Then for every a є R \ {0, 1), the 1st-order differential equation is called Bernoulli equation. It is a nonlinear ordinary differential equation. (a) Use the literature and describe in brief steps a method to find a solution of equation (1). Hint: See Trench, p.63 (b) Find all solutions to the following two differential equations. Use Mathematica...
Let F be the equation y=e^5x, let G be the equation x= 7, and let H be the equation y=1 . Find the area of the region enclosed by the graph of these equations.(Use symbolic notation and fractions where needed.) area= (b), Let F be the equation y= sin(11 x), and let G be the equation y= cos(11 x). Find the area of the region enclosed by the graphs of these equations if 0 less than equal to x less...
1. Let y = f(x) be the solution to the differential equation = y - x. The point (5,1) is on the graph of the solution to this differential equation. What is the approximation for f() if Euler's Method is used, starting at x = 5 with a step size of 0.5?
Problem # 2: The objective is to solve the following two nonlinear equations using the Newton Raphson algorithm: f(x1 , X2)=-1.5 6(X1-X2)=-0.5 Where: f (x,x2x-1.lx, cos(x,)+11x, sin(x,) f2(X1-X2)-9.9X2-1.1x, sin(%)-iïx, cos(%) 1. Find the Jacobian Matrix 2. Lex0, x 1, use the Newton Raphson algorithm to a find a solution x,x2 such that max{_ 1.5-f(x1, X2 ' |-0.5-f(x1, X2)|}$10
7. Show that the equation f(x) = x^3 + 3x^2 - 9x + 7 = 0 has a solution for some x is E(-6; -5). Apply Newton’s method with an initial guess x0 = -5 to find x2. 8. Find the intervals of increase and decrease of the function x2e^-2x. 9. Sketch the graph of the curve y = x3 + 3x2 - 9x + 7. Be sure to find the intervals of increase, decrease and constant concavity and all...
The equation is 9. Find a general solution x(t) of the equation in example 6 (week 10) when nl-1 . k-10 and the driving force f(t)-1-t, 0 < t < 2, f(t + 2) = f(t) d xia 9. Find a general solution x(t) of the equation in example 6 (week 10) when nl-1 . k-10 and the driving force f(t)-1-t, 0
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i + 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1, f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the data point (0, 3), find a Newton form for the Lagrange polynomial interpolating all 5 data points. 3. (25 pts) Let (r,, f()), 0,3, be data...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
I need the solution of this asap. Thanks 7. Let X Nu, E), where u= 0 and = Let Y = X3 + x 2X2 X3 - X1/ i) What is the distribution of Y? ii) Which components of Y are independent of each other?