#
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2003
#
# file:  sqrt_approx
#
# Write the Taylor series expansion of sqrt(1+h), find the 
# approximation to sqrt(1+h) for h = 0.00001 and h = -0.00001.
# Asking for the calculation to be done to 40 decimal digits:

 y := taylor(sqrt(1+h), h=0);
 p := convert(%, polynom);
 Digits := 40;
 subs(h=0.00001, p);
 evalf(%);
 subs(h = -0.00001 ,p);
 evalf(%);

# Verification of the accuracy of the answer:
 x := sqrt(1.00001);