Consider the function fr(x)=√1+0.5 sin (r) — ¹0 Find the values of r that maximize and minimize the area under the curve. A, - √1+0.5 sin (r) L Des x10 dx
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Please attempt this problem on python. Doesn't even need to be right! My professor asked us to try it
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- Consider the function f(x) = 1 3x+1 . We approximate f(x) by the Lagrange interpolating polynomial P₂ (x) at the points xo = 1, x₁ = 1.5 and.x₂ = 2. A bound of the theoretical error of this approximation at x = 1.8 is:Develop a program to obtain first-derivative estimates for unequally spaced data. Test it with the following data: X f(x) 1 1.5 1.6 2.5 3.5 0.6767 0.3734 0.3261 0.08422 0.01596For the function f: Z Z prove or disprove whether f is injective and/or surjective f(x) = 4x –6 %3D
- For each of the following pairs of functions ff and gg, circle one of the answers f \in o(g), f \in \Theta(g),fEo(g),fE0(g), or g \in o(f)g€o(f) f(n) = 2", g(n) = (;) Oƒ € o(g9) Oƒ€ 0(g) O gE o(f) %3D %3D i=log2 n f(n) = E" 2', g(n) =n Oƒ € o(g) Oƒ€ 0(g) O gE o(f) %3D %3D f(n) = (210 + 3n)², g(n) = n² Oƒe o(g) Oƒ€ 0(g) Oge o(f) %3D %3D1. Given the function, f(A, B, C, D,E) = E m(prime number:"5 input variables that generates output 1 if and only if the number of l's in the input is prime number"), minimize it using the Karnaugh map method.Two small charged objects attract each other with a force F when separated by a distance d.If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2,the force becomes?
- Determine whether each of these functions is a bijection from ℝ to ℝ. If it is, write the inverse function. f(x) = 3|x| − 4Determine whether each of these functions is a bijection from R to R. Show all the step to finding the injective, surjective and bijective. а. f(x) %3D 3x + 4 b. f(x) = x3 + 7x3 is O(g(x)) for each of the ff. functions g(x) EXCEPT O g(x) = x² O g(x) = x° O g(x) = 3* O None of the choices
- Find the asymptotes of the following curve: y = x+2 x+3f(n) = 2", g(n) = 2.01". v.In your preferred programming language, code the Newton-Raphson method to find the stationary points of a nonlinear function. Please include your code with your hw submission. Use your implementation to find the stationary points of the following non-linear functions W:(x1, 82), W2(x1, T2), and W3(x1, 82): W: (x1, 2) = xỉ + x W2(x1, #2) = rỉ + x W3(x1, 2) = x} – x† + x3 – x3 + 0.1x,r2 %3| starting the following two initial guesses in each case: • x1 = 0.1, x2 = 0.1 • x1 = 1.0, x2 = 1.0 For W1(x1, x2), W2(x1, X2), and W3(x1, 02) and for each initial guess, please report: 1. The function value. 2. The coordinates x1 and x2 of the function stationary point. 3. The plot of the function value as a function of the Newton-Raphson iteration. Can anyone help me set this up? I will be using MATLAB but am new to this type of stuff so any help would be appreciated