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14 Typeset: ∇2 f (x, y) = ∂2f ∂x2 + e−x eiπ + 1 = 0 x0 x20 TEXbook: 128–130 and ^ in x0 2 x 2x . ∂2f ∂y 2 . A similar method is used for summations and integrals. The input of $\sum {k=1}^n x n k^2$ will give k=1 k 2 , and $\int 0^x f(t) dt$ will give 0 f (t)dt. Another use of this type of input is for expressions involving limits. You can use n $\lim {n\to \infty}({n+1 \over n})^n = e$ to get limn→∞ ( n+1 n ) = e. 15 Typeset the following expression: limx→0 (1 + x) x = e. 16 Typeset: The cardinality of (−∞, ∞) is ℵ1 .

For one, the column size must be set before the entries are known. Also, even though in one case we wanted the third column to be boldface, it had to be specified in each line. These problems can be handled more easily by using the \halign environment. The general pattern in the \halign is as follows: \halign{