Prove that the following sequences are convergent, and find their limits. x(k) = (1/k, e'-k, –2/k²)' x) = (e-* cos k, k sin(1/k), 3 + k-2)' a. b.

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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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3.
Prove that the following sequences are convergent, and find their limits.
x() = (1/k, e'-k, –2/k²)'
x(k) = (e-k cos k, k sin(1/k), 3 + k-2)'
а.
b.
x(k) = (ke-k*, (cos k)/k, /k² | k k)'
x(k) = (e!/k, (k² + 1)/(1 – k²), (1/k²)(1+3+5+ .+ (2k – 1)))'
с.
d.
Transcribed Image Text:3. Prove that the following sequences are convergent, and find their limits. x() = (1/k, e'-k, –2/k²)' x(k) = (e-k cos k, k sin(1/k), 3 + k-2)' а. b. x(k) = (ke-k*, (cos k)/k, /k² | k k)' x(k) = (e!/k, (k² + 1)/(1 – k²), (1/k²)(1+3+5+ .+ (2k – 1)))' с. d.
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