(a) Determine whether the set of functions is linearly independent on the interval (-∞, ∞). f₁(x) = x, f₂(x) = x − 1, f3(x) = x + 3
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- 1. Find the linearization of x3 − x at a = 2.find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. 1. ƒ(x) = x2 + 2x, a = 0.1 2. ƒ(x) = x-1, a = 0.9 3. ƒ(x) = 2x2 + 3x - 3, a = -0.9 4. ƒ(x) = 1 + x, a = 8.11. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example
- Find the linearization L(x)of the function at a .Prove that if y1 and y2 are linearly independent solutions to thehomogeneous, then the functions y3 = y1 + y2 and y4 = y1 - y2 are also linearly independent solutions.Determine whether the functions y1 and y2 are linearly dependent on the interval (0,1)
- 12 help use variation of parameters to finda general solution to the differntial equation given the function y1 and y2 are linearly independent solutions to the corresponding homogenous equation for t>0find a linearization at a suitably chosen integernear a at which the given function and its derivative are easy to evaluate. ƒ(x) = 2x2 + 3x - 3, a = -0.9f1 (x) = ex+a, f2 (x) = ex+b, f3 (x) = ex+ca,b,c are constants. Using Wronskian, determine if the functions above are linearly dependent or not. Full solution is required.