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Check all statements that are true. If p is a polynomial of degree n, and q is a polynomial of degree m, and n-m, then p is of order q. All power functions f(x)=x", where n is a real constant, are O(e*). The triangle inequality is the most common algebraic tool for rigorously proving order relationships.

Check all statements that are true. If p is a polynomial of degree n, and q is a polynomial of degree m, and n-m, then p is of order q. All power functions f(x)=x", where n is a real constant, are O(e*). The triangle inequality is the most common algebraic tool for rigorously proving order relationships.

Advanced Engineering Mathematics
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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need helping understanding this concept And why each statement is false or true QUESTION 1 Check all statements that are true. ☐ If p is a polynomial of degree n, and q is a polynomial of degree m, and n=m, then p is of order q. All power functions f(x)=x", where n is a real constant, are O(e*). The triangle inequality is the most common algebraic tool for rigorously proving order relationships. f(x)=sin(x) is of order 1. There is a "largest order", i.e. there is some function g so that all other functions f are O(g). The triangle inequality says that for all real numbers and b. la + bl<lal + lbl If a and b are two positive numbers, then the following is true: axis of order b* exactly when a and b are equal. axis O(b*) exactly when a<b. a is (b*) exactly when a>b. f(x)=x is : 0(x²) If two functions are of order g, then so is their sum. f(x) Iff and g are functions defined for all positive real numbers and if lim x →∞ g(x) f(x)=5x is of order 3x. f(x)=x is (√√x) If p is a polynomial of degree n, and q is a polynomial of degree m, and n<m, then p is O(q). If two functions are O(g), then so is their sum. 0 0 0 00 = C where C is a positive constant, then f is of order g. hand written plz
Transcribed Image Text:need helping understanding this concept And why each statement is false or true QUESTION 1 Check all statements that are true. ☐ If p is a polynomial of degree n, and q is a polynomial of degree m, and n=m, then p is of order q. All power functions f(x)=x", where n is a real constant, are O(e*). The triangle inequality is the most common algebraic tool for rigorously proving order relationships. f(x)=sin(x) is of order 1. There is a "largest order", i.e. there is some function g so that all other functions f are O(g). The triangle inequality says that for all real numbers and b. la + bl<lal + lbl If a and b are two positive numbers, then the following is true: axis of order b* exactly when a and b are equal. axis O(b*) exactly when a<b. a is (b*) exactly when a>b. f(x)=x is : 0(x²) If two functions are of order g, then so is their sum. f(x) Iff and g are functions defined for all positive real numbers and if lim x →∞ g(x) f(x)=5x is of order 3x. f(x)=x is (√√x) If p is a polynomial of degree n, and q is a polynomial of degree m, and n<m, then p is O(q). If two functions are O(g), then so is their sum. 0 0 0 00 = C where C is a positive constant, then f is of order g. hand written plz
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