4. Absolute and Relative Error (10 pts) Hyperbolic sine, f(x)=sinh(x), has the following Taylor polynomial approximation (i.e. a truncated Taylor series): f~(x)=x+6x3. (a) Confirm that the approximation is a Taylor polynomial based off the point a=0. (b) Compute the absolute and relative error between f(x) and f~(x) at x=0.1,1.0,10.0. Plotting with matplotlib ( 10 pts) Using X = NP.LINSPACE (0,10,200) in python with the numpy library (IMPORT NUMPY AS NP), plot f(x) and f~(x) from Problem 4 using the matplotlib library. Plot f(x) using a blue line ('-b') and the f~(x) with a dotted red line (':r')