Finding the Radius of Convergence In Exercises 49–52, find the radius of convergence of (a) f(x), (b)
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- pdf.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_forwardDerive 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_forwardDiscuss limit(n →∞)fn on B and C for fn(x)= ∑nk=1xk; B=(-1,1); C=[-a,a], |a|<1 fn(x)=1/(1+nx); C=[0, ∞)arrow_forward
- Find the intervals of convergence of f(x), f '(x), f"(x), and f(x) dx. Include a check for convergence at the endpoints of the interval. (Enter your answer using interval notation.) (-1)" + 1(x – 2)" Σ f(x) = n = 1 (a) n2" f(x) (b) f'(x) (c) f"(x) f(x) dxarrow_forwardLetting a and 3 be two positive constants such that B> a, •+∞ In(B/a) a-B converges to 1 - In(3/a) converges to converges to Diverges dx (ax+1)(Bx+1) In(a/B) a-B converges to 1+ converges to 1+ In(a/B) a-ß In(B/a) B-α converges to 1 - In(a/B) converges to In(a/B) O Oarrow_forwardAdvanced calculus 1arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage