I3

(c) The add-on MTH229 package defines some convenience functions for this class. This package must be loaded during a session. The command is using MTH229, as shown. (This needs to be done only once per session, not each time you make a plot or use a provided function.) For example, the package provides a function tangent that returns a function describing the tangent line to a function at c = c. These commands define a function tline that represents the tangent line to f(x) = sin(r) at x = 1/4: | using MTH229 f (x) = sin(x) | c = pi/4 tline (x) = tangent (f, c) (x) (To explain, tangent (f, c) returns a new function, for a pedagogical reason we add (x) on both sides so that when tline is passed an x value, then this returned function gets called with that x.) The tangent line has the from y = max + b. Use tline above to find b by selecting an appropriate value of x: (d) Now use tline to find the slope m. Hint..(c) Let a function be defined by: f(x) = 2 cos (3x - 1) + x log(x) 2-x2 (d) What is the value of f(3)? 2.94168 (e) What is the value of f(/2)? 23.77