15 4 23 Let fbe a function having derivatives of all orders for all real numbers. Selected values of fand its first four derivatives are shown in the table above. 6. a) Write the second-degree Taylor...
Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above. (a) Write the second-degree Taylor polynomial for f about x = 0 and use it to approximate f(0.2). (b) Let g be a function such that g(x) =f(x3). Write the fifth-degree Taylor polynomial for g', the derivative of g, about x = 0. (c) Write the third-degree Taylor polynomial for f about x =...
A function f, which has derivatives for all orders for all real numbers, has a 3rd degree Taylor polynomial for f centered at x = 5. The 4th derivative of f satisfies the inequality f^(4)(x) ≤ 6 for all x the interval from 4.5 to 5 inclusive. Find the LaGrange error bound if the 3rd degree Taylor polynomial is used to estimate f(4.5). You must show your work but do not need to evaluate the remainder expression.
5001 1 +- +-- 400 300 1200 100 -0 0.5 -100 Graph of rs 3. Let f and g be given by f(x)- xe and g(x)-(). The graph of f, the fifth derivatve of f is shown above for (a) write the first four nonzero terms and the general term of the Taylor series for e, about x = 0 . Write the first four nonzero terms and the general term of the Taylor series for f about x 0....