Finding the Radius of Convergence In Exercises 49–52, find the radius of convergence of (a) f(x), (b)
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- Derive difference formulas for the first, second, and third derivatives of a function f at a point x, using interpolation at f(x-h), f(x), f(x + h), and f(x + 2h) Find the order of convergence for all the approximationsarrow_forwardpdf.6 öyölas -> find (f-g)(x) (f+g)x) f.g)). ) Find (f/g)(x) and (8/f)(x) for the functions given by f(r) = r and g(x) = /4-. Then find the domains of f/lg and g/f. ★******* ******************************************************** Composition of Functions Definition of Composition of Two Functions- The composition of the function of f with the function g is: (fo g) (x) =f(g (x)). The domain of (fo g) is the set of all x in the domain of g such that g (x) is in the domain of f. For instance, iff (x)= x² and g (x) = x+1, the composition of f with g is: f(g (x)) = (x+1) Abe (Н.W) If f(x) = 4 - x² & g(x) = Vx then find (fog)(), (gof)(x) x+8 If f(x) = 3x - 8 & g(x) = then find (fog)(x). (gof)cx) 3 and is (fog)c).(gof) are equal ?? x2 - 2x & g(x) = 3-x then solve the equations: a) (fog)) = 0 & b) (gof)m + x +5: If f(x) = x - 9 & g(x) = 2x - 5 then find the solution for (fog)(x) <0 If fx)=x2-2x-3 & g(x) = 1X then find: a) (fog)(x) & b) (gof)) T F)%3 & g(x) = then find b) (gof)< x+2 a)…arrow_forwardFind an integer n so thạt the interval of the form [n , n+1] contains a solution to the equation x2 + = 1. * The integer is n = (a) if f (x) = x² + L - 1, then f (n) = and f(n+1) = (b) The function f is continuous on the interval(s) O (-0, ∞) O (-0, a) O (a, 0) O (-∞, a) U (a, ∞) O (-0, b] U [b, ∞) Choose the largest set possible and give the values for a and/or b. Enter DNE in any empty blank. b = The theorem that tells us that the solution must be in the interval [n, n+1] is the symbolic formatting help (you must write out the full name, correctly spelled).arrow_forward
- convergencearrow_forwardFind an integer n so that the interval of the form [n , n+1] contains a solution to the equation x2 + - = 1 . The integer is n = (a) if f (x) = x² + 1 - 1, then f (n) = and f (n+1) = (b) The function f is continuous on the interval(s) O (-∞, ∞) O (-∞, a) О (а, о) O (-∞, a) U (a, o) O (-∞, b] U [b, ∞) Choose the largest set possible and give the values for a and/or b. Enter DNE in any empty blank. a = b = The theorem that tells us that the solution must be in the interval [n, n+1] is the (you must write out the full name, correctly spelled). symbolic formatting helparrow_forward★ Evaluate. [(sec*(x)) dxarrow_forward
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