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Little N notation • Let f(x) and g(x) be nonnegative real-valued functions on the positive real numbers, and suppose that g(x) is strictly positive for all x sufficiently large • We define f(x) = w(g(x)) if for every constant c > 0 there exists a constant d such that f(x) > cg(x) for all x > d. • Another way to say that is: f(x) = w(g(x)) if f(x) limx→g(x) = ∞. • Example: x? = w(x1.9), but x² + 5vxt w(0.01x²). 5x + ex = w(2×), but 7x + 2× f w(e*). Problem: Prove or disprove: n" = w(n!)

Little N notation • Let f(x) and g(x) be nonnegative real-valued functions on the positive real numbers, and suppose that g(x) is strictly positive for all x sufficiently large • We define f(x) = w(g(x)) if for every constant c > 0 there exists a constant d such that f(x) > cg(x) for all x > d. • Another way to say that is: f(x) = w(g(x)) if f(x) limx→g(x) = ∞. • Example: x? = w(x1.9), but x² + 5vxt w(0.01x²). 5x + ex = w(2×), but 7x + 2× f w(e*). Problem: Prove or disprove: n" = w(n!)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Little 2 notation • Let f(x) and g(x) be nonnegative real-valued functions on the positive real numbers, and suppose that g(x) is strictly positive for all x sufficiently large • We define f(x) = w(g(x)) if for every constant c >0 there exists a constant d such that f(x) > cg(x) for all x > d. Another way to say that is: f(x) = w(g(x)) if f(x) g(x) = 0. ► Example: x? = w(x!.9), but x² + 5/x+ w(0.01x²). w(2*), but 7x + 2* # w(e*). Problem: Prove or disprove: n" = w(n!) ► 5x + eX =
Transcribed Image Text:Little 2 notation • Let f(x) and g(x) be nonnegative real-valued functions on the positive real numbers, and suppose that g(x) is strictly positive for all x sufficiently large • We define f(x) = w(g(x)) if for every constant c >0 there exists a constant d such that f(x) > cg(x) for all x > d. Another way to say that is: f(x) = w(g(x)) if f(x) g(x) = 0. ► Example: x? = w(x!.9), but x² + 5/x+ w(0.01x²). w(2*), but 7x + 2* # w(e*). Problem: Prove or disprove: n" = w(n!) ► 5x + eX =
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