Second Round Dutch Mathematical Olympiad
... facing up for each of these 32 situations and writes down all results. If Raymond adds up these 32 numbers, what will be the final result? ...
... facing up for each of these 32 situations and writes down all results. If Raymond adds up these 32 numbers, what will be the final result? ...
AP Calculus Multiple Choice: BC Edition – Solutions
... The first series is a geometric series with common ratio 1/2, and thus this converges. The second series can be compared to a p-series with p = 2, and thus it too converges. The sum of two convergent series is also convergent. This leaves choices I and III still valid, but we need to examine them in ...
... The first series is a geometric series with common ratio 1/2, and thus this converges. The second series can be compared to a p-series with p = 2, and thus it too converges. The sum of two convergent series is also convergent. This leaves choices I and III still valid, but we need to examine them in ...
FABER FUNCTIONS 1. Introduction 1 Despite the fact that “most
... Theorem 2. If (fk )k∈N is a sequence of continuous functions on [a, b] that converge uniformly to some f in [a, b], then f is continuous in [a, b]. Proof. Let (fk )k∈N be a sequence of functions that satisfy the hypotheses. Uniform convergence then gives us: (∀ε > 0)(∃N ∈ N)(∀n ≥ N )(||fn − f || < ε ...
... Theorem 2. If (fk )k∈N is a sequence of continuous functions on [a, b] that converge uniformly to some f in [a, b], then f is continuous in [a, b]. Proof. Let (fk )k∈N be a sequence of functions that satisfy the hypotheses. Uniform convergence then gives us: (∀ε > 0)(∃N ∈ N)(∀n ≥ N )(||fn − f || < ε ...
Math 331–Homework #6 Reality-check problems.
... Reality-check problems. Not to write up; just ensure that you know how to do them. I. Verify the following binomial coefficient identites hold for all complex numbers x and all integers k: ...
... Reality-check problems. Not to write up; just ensure that you know how to do them. I. Verify the following binomial coefficient identites hold for all complex numbers x and all integers k: ...
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Convergence of Taylor Series
... Given known Taylor Series, other series can be obtained using the following operations term by term … ...
... Given known Taylor Series, other series can be obtained using the following operations term by term … ...
MATH 1920 --- CALCULUS II COURSE SYLLABUS INSTRUCTOR
... PREREQUISITE: This course requires a grade of C or better in Math 1910 or its equivalent. Familiarity with graphing calculators (TI-83, 84, etc) is required. You may not use graphing calculators with symbolic manipulation software (DERIVE, MAPLE, etc.) on exams. TEXTBOOK: Calculus: Early Transcenden ...
... PREREQUISITE: This course requires a grade of C or better in Math 1910 or its equivalent. Familiarity with graphing calculators (TI-83, 84, etc) is required. You may not use graphing calculators with symbolic manipulation software (DERIVE, MAPLE, etc.) on exams. TEXTBOOK: Calculus: Early Transcenden ...
