Nonconvergence to f Consider the function
a. Use the definition of the derivative to show that f'(0) = 0.
b. Assume the fact that f(k)(0) = 0, for k = 1, 2, 3,.... (You can write a proof using the definition of the derivative.) Write the Taylor series for f centered at 0.
c. Explain why the Taylor series for f does not converge to f for x ≠ 0.
Part2: 8. Elusive(adj):somethingisdifficulttofind,catch,remember,orachieve.Example:Jane’s characteristiciselusivethesedays. 9. Nuances(noun):smallofsubtledistinction.Example:Menshouldcomplementevery timewomenmakeanuanceontheirlooks. 10. Anomalies(noun):somethingthatisdifferentfromthestandard.Example:The anomalies,intheweatherforecastrecently,suggestedthattherewouldbeastorm....