Application #2:  Use a  differential  to estimate  cos(56):

•  We know the value of cos(60);

• Let F(x) = cos(x).   So x is increased from 60 to 56.

(Step by Step Solution -- part A) :

1.  y1 : cos(%Pi/3);     returns  RESULT
2.  block(define(df(x,h),diff(cos(x),x)*h))     returns  RESULT
3.   h is -4 degrees.   Converting -4 degrees to radians, we have

- 4 =  h: - 4*%Pi/180     returns  RESULT

4.  Sodf(%Pi/3,h),numer=true;     returns RESULT
5.  Compare withcos(%Pi/3+h)-cos(%Pi/3),numer=true;     returns RESULT

Exercise:  Salas & Hille's Calculus (3.9 #11, #12)