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- Find the 3rd degree Taylor polynomial for f (x) =lnx at the value for a=14. Let the function x(1) be given by the conditions x (0) = 1 and x (1) = 1x(1) + 2[x(1)]² Determine the second order Taylor polynomial for x(1) about / == = 0. 5. Establish the approximationfind the taylor polynomials of order 0 1 2 and 3 generated by f(x) =1/(x+5) at x=0
- Find the Taylor polynomial of degree 2 centered at a=π that approximates f(x)=cos(5x) P2(x)=Let f(x) = cos(2x)(a) Compute p2(x) (the second order Taylor polynomial) at a = π/8.(b) For the function in part (a), use the Taylor estimation theorem to find an upper bound for theapproximation error|R2(x)| = |f(x) − p2(x)|if x lies in the interval [0, π/4]find the Taylor polynomials of orders 0, 1, 2, and 3generated by ƒ at a.3. ƒ(x) = ln x, a = 1 4. ƒ(x) = ln (1 + x), a = 0