Error Approximations: The function F(x)=e^(-2x) is approximated by the polynomial f(x)is approximately 1-2x+2x^2-(4/3)x^3. For what x-values will this approximation have an error of less than .001?

Question

turingtest · Answer

http://www.wolframalpha.com/input/?i=plot+%7Ce%5E%28-2x%29-1%2B2x-2x%5E2%2B4x%5E3%2F3%7C%3D0.001

turingtest · Answer

looks to be within about 0.2 of x=0 http://www.wolframalpha.com/input/?i=solve+%7Ce%5E%28-2x%29-1%2B2x-2x%5E2%2B4x%5E3%2F3%7C%3D0.001 I don't know how to solve it analytically though

anonymous · Answer

oh i see! makes sense. Thanks you!! :D