 | William Holding Echols - Calculus - 1902 - 536 pages
...£A(*') + • • • £/.(*'), =/,(£*') + • • • A(£^), =/,(-»•) + • • - +/.(*) = <t>(x). II. The product of a finite number of continuous functions is a continuous function in any common interval of continuity of these functions. If 0(*) =/,(•*) •/,(*) • • -/.(*),... | |
 | Edgar Jerome Townsend, George Alfred Goodenough - Calculus - 1908 - 492 pages
...functions is a continuous function throughout any interval in which all the functions are continuous. (b) The product of a finite number of continuous functions is a continuous function throughout the common interval of continuity. (c) Every integral rational algebraic (unction is continuous... | |
 | Thomas Murray MacRobert - Functions - 1917 - 330 pages
...THEOREM 1. The sum of a finite number of continuous functions is a continuous function. THEOREM 2: The product of a finite number of continuous functions is a continuous function. THEOREM 3. The ratio of two continuous functions is continuous except for values of z which make the... | |
 | Edgar Jerome Townsend - Functions - 1928 - 426 pages
...of a limit, the laws of operation with limits apply to such functions. Thus the sum, difference, and product of a finite number of continuous functions is a continuous function. The quotient of one continuous function by another is continuous at any point at which the denominator... | |
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The product of a finite number of continuous functions is a continuous function so long as all factors remain finite. 