Guide to LaTeX (4th Edition) (Tools and Techniques

5.4. Additional elements 141
Exercise 5.17: The following equations are to be broken as shown:
arcsin x = − arcsin(−x) = π
− arccos x = arccos 1 − x
2 2
x
= arctan √
1 − x2 =
√
1 − x2 arccot
x
∂f (x, y) ∂f (x, y)
f (x + h, y + k) = f (x, y) +
h + k
∂x
∂y
+ 1
2 ∂ f (x, y)
2 ∂x2 h 2 + 2 ∂2f (x, y)
∂x∂y kh + ∂2f (x, y)
∂y 2
k 2
+ 1
1
{· · · } + · · · + {· · · } + Rn
6 n!
Note on possible error messages:
Long formulas with many sets of logical brackets, especially
deeply nested ones, will almost always contain errors at first. The
cause is often brackets that have been incorrectly ordered or overlooked.
If L AT E X produces error messages during formula processing, which
the beginner is not able to interpret correctly (error messages are
described in detail in Appendix C), he or she should check the bracket
pairing very carefully in the formula text. Some text editors can do
the search for the matching bracket, which greatly simplifies the task.
If the error is not found in this way, one can try pressing the return
key at the error message in order to proceed with the processing. The
resulting printout can indicate where things may have gone wrong.
(5.6)
(5.7)
Exercise 5.18: The eqnarray environment inserts additional spacing where the
column separation character & appears. This is undesirable when an equation is
to be broken and aligned on + or − within a long summation. For example:
The inverse function of the polynomial expansion y = f (x) = ax + bx 2 + cx 3 +
dx 4 + ex 5 + f x 6 + · · · (a = 0) begins with the elements
x = ϕ(y) = 1
y
a
−
b
a3 y 2 + 1
a5 (2b2 − ac)y 3
+
1
a7 (5abc − z2d − f b 3 )y 4
+
+
1
a9 (6a2bd + 3a 2 c 2 + 14b 4 − a 3 e − 21ab 2 c)y 5
1
a11 (7a3be + 7a 3 cd + 84ab 3 c − a 4 f −
28a 2 b 2 d − 28a 2 bc 2 − 43b 5 )y 6 +· · ·
Select a value for the declaration \arraycolsep (Section 4.8.2) such that the
distance between the + and − and the break points are as near as possible to
those in the rest of the formula.