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CAn you give an example with Taylor series approximation. I've watched several videos on youtube but still dont understand it
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Is it possible to get a example which shows this applied to a model
- Find Fourier transform of the n-th derivative f(n) of a smooth function f with fast decay at infinity.The equation def ined by: f„(x) y) +f „-1(x) y" -'+ ...+f ,: ,(x) y (2) +f ,(x)y'+f ,(x)y=G(x) with coefficient f_(x) #0 and for all n, f_ are functions on x, is called...... The general form of second order ODE with .variable coefficients The general form of Higher order ODE with .constant coefficients The general form of Second order ODE with constant .coefficients The general form of Higher order ODE with .variable coefficientsExpand f(z) = 1 (z-1)(z-2) -; 0Let f be a function with derivatives of all orders throughout some interval containing a as an interior point. Then the Taylor series generated by f(x) at x = 0 is: f"" (0) 3! f'(0) f(x) = f(0) + -x+ 1! 2! f(x) at x = a is: And the Taylor series generated f(x) = f(a) + f'(a) 1! +2 TT d) f(x) = sinx, a = 4 e) f(x)=√x, a = 4 + f" (a) (x a) + ·(x − a)² + 2! x3 f"" (a) 3! + ... (x − a)³ + ... - 1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a.The logistic function given by f (x) 1 is a sigmoid (s-shaped) function useful in many 1+e-* areas of mathematics and computer science. The function f is a bijection, whose domain is R and range is (0, 1). (a) function g : (0, 1) → (a, b), show that |R| = |(a, b)|. Given an arbitrary interval (a, b), by using the composition of f with an appropriate (b) By using part (a) show that [a, b] = (a, b). (c) The derivative of f is equal to f'(x) = f(x)f(-x). Show that f' is not one-to-one.Expand f(z) = Z (z-1)(3-z) -; Iz-11>2.Let f'(x)=(x-1)(x-3). Then f is increasing on a) (-∞,1]U[3,00) b) (-∞,2] c) [1,3] d) [2,0⁰)Let fn, f be real functions on S2. Show ∞ ∞ ∞ {w: fn(w) + f(w)} = UNU {w: | fn(w) - f (w)| ≥ } }. k=1N=1n=NLet f be a function with derivatives of all orders throughout some interval containing a as an interior point. Then the Taylor series generated by f(x) at x = 0 is: ƒ'(0) f(x) = f(0) + -x + 1! f"(0) f"" (0) -x² +: 3! 2! And the Taylor series generated by f(x) at x = a is: f(x) = f(a) + 1 == a = 2 ) f'(a) 1! c) f(x) = f"(a) 2! 1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e²x, a = 0 b) f(x) = lnx, a = 1 π d) f(x) = sinx, a = = 4 e) f(x) = √x, a = 4 -x³ + (x − a) + -(x − a)² + · (x − a)³ + · f""'(a) 3!how to find the recursion relation of xy''+y'+xy=e^x, x0=1Prove that y = e-3* (Acos 5x – Bsin 5x) + Cx; A, B and C are arbitrary constants wil ealto y"(17x + 3) + y"(102x + 1) + 578(xy' - y) = 0 If you use eliminating arbitrary constantQ-2) Prove that converting the Higher-Order derivatives to the finite difference formula would be: f (x;) – 2f (xi-1) +f(xi-2) 1) f"(x¡) = "Backward Method" (Ax)2 f (x;) – 3f (xi-1) + 3f (xi-2) – f(xi-3) (Ax)³ 2) f'(x;) = "Backward Method" f(xi+3) – 3f(x;+2) + 3f(x;+1) – f(x;) (Ax)3 3) f"'(x;) = "Forward Method"SEE MORE QUESTIONS