¡¥es, Infinite Series, Improper Integrals. Definition. A function f whose domain is the set of all positive integers 1,2,3.... is called an infinite sequence. The function value f(n) is called the nth term of the sequence. Definition. A sequence {f(n)} is said to have a limit L if, for every positive number ¥å, there is another positive number N (which
¡¥5.4. Substitution Theorem for Integrals. Assume g has a continuous derivative g` on an open interval I. Let J be the set of values taken by g on I and assume that f is continuous on J. Then for each x and c in I, we have . - P(x) = right-hand, Q(x) = left-hand, R(x) = P[f(x)] Point. Integration by Parts. - ¡ò u dv = uv - ¡ò v du. Theorem. 5.5. Second