p. 20, #1, 2, 5, 6, 7

(* #1 *)
xhat=2.62
x=2.615
error[x_, xhat_]:=xhat-x
relativeError[x_, xhat_]:=error[x,xhat]/x
re=relativeError[x,xhat]
relativeError[Exp[x],Exp[xhat]]

(* #2 *)
xhat=1.4
(* x is in the interval [1.3,1.5] *)
{relativeError[1.5,xhat],relativeError[1.3,xhat]}

(* #5 *)
(* Log[10,2] approx w/10 *)
N[Log[10,2]]

(* #6 *)
e1=(y1-y)
e2=(y2-y)
r1=e1/y
r2=e2/y
decimalsOfAccuracy[e_]:=-Log[10,e]
digitsOfAccuracy[re_]:=-Log[10,re]
Simplify[decimalsOfAccuracy[e2/3]-decimalsOfAccuracy[e2]]
Simplify[digitsOfAccuracy[r2/3]-digitsOfAccuracy[r2]]

(* #7 *)
f[h_]:=1/(1-h)
fhat[h_]:=1+h*(1+h)
h=.21
hhat=.2
propogatedError[h_,hhat_]:=f[hhat]-f[h]
computationalError[h_,hhat_]:=fhat[hhat]-f[hhat]
totalError[h_,hhat_]:=computationalError[h,hhat]+propogatedError[h,hhat]

computationalError[h,hhat]
propogatedError[h,hhat]
totalError[h,hhat]