3. Prove that 3kN, Vn N, [n>k][1000m² + 10 ≤ n²]. Hints: you can divide both sides by n² and preserve the inequality, since n2 is always positive. Re- minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note that 10/n2 <1 if n ≥ 4. Justify every step.
3. Prove that 3kN, Vn N, [n>k][1000m² + 10 ≤ n²]. Hints: you can divide both sides by n² and preserve the inequality, since n2 is always positive. Re- minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note that 10/n2 <1 if n ≥ 4. Justify every step.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with these questions. I am having trouble understanding what to do. Please show all you work
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![4. Let R+ be the set of positive real numbers and N+ be the set of positive natural numbers. Prove that
Va € R+, Vb € R+, Vp₁ € N+, Vp2 € N+, [P1 ≤ p2] ⇒ an³¹ € 0 (bn³².)
You may not use, without proof, any properties of big-Oh, other than its definition. Justify every step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e1fe2dc-a274-4b26-849f-c30d3fc856c1%2Fd8af748b-3c10-4d85-9d8f-11a2b5a89e52%2F9639767_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Let R+ be the set of positive real numbers and N+ be the set of positive natural numbers. Prove that
Va € R+, Vb € R+, Vp₁ € N+, Vp2 € N+, [P1 ≤ p2] ⇒ an³¹ € 0 (bn³².)
You may not use, without proof, any properties of big-Oh, other than its definition. Justify every step.
![3. Prove that
k = N, Vn Є N, [n>k][1000m² + 10 ≤ n²].
Hints: you can divide both sides by n² and preserve the inequality, since n² is always positive. Re-
minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note
that 10/n2 <1 if n ≥ 4. Justify every step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e1fe2dc-a274-4b26-849f-c30d3fc856c1%2Fd8af748b-3c10-4d85-9d8f-11a2b5a89e52%2F1e4cu1r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Prove that
k = N, Vn Є N, [n>k][1000m² + 10 ≤ n²].
Hints: you can divide both sides by n² and preserve the inequality, since n² is always positive. Re-
minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note
that 10/n2 <1 if n ≥ 4. Justify every step.
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