Consider a function f(x) = 25x ଷ − 6x ଶ + 7x − 88. Using the Taylor series expansions of this functions from zero- through third-order, predict the value of f(x) with x = 3 using a base point of x଴ = 1.0. For each such Taylor series approximation, list the following: (i) Approximate value of f(3.0).
(ii) On what order of the step size ‘h’ is the truncation error?
(iii) Compute the true percent relative error,t , for each approximation.

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.