Math Problem Statement
Calculate the limits of each of the following sequences. If a sequence converges, enter its limit. If a sequence diverges, enter the letter X.
a. {sin(5n)/n} b. {sin(4n)/n} c. {sin(π(6n+1)/2) d. {nsin(6πn)}
Solution
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Math Problem Analysis
Mathematical Concepts
Limits of Sequences
Trigonometric Functions
Oscillating Functions
Formulas
lim (n→∞) sin(kn)/n = 0 (for bounded sin(kn))
lim (n→∞) nsin(kπn) = 0 (for kπn multiples of 2π)
Sine periodicity: sin(x + 2πk) = sin(x)
Theorems
Boundedness of Sine and Cosine
Squeeze Theorem (for oscillating functions)
Periodicity of Trigonometric Functions
Suitable Grade Level
Grades 11-12
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