Check all statements that are true.

f(x) = sin(x) is big-O of 1.

All power functions f(x)=x, where n is a real constant, are O(e).

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.

f(x)=x is O(x).

The triangle inequality is the most common algebraic tool for rigorously proving order relationships.

f(x)=5x is of order 3x.

f(x)=x is (x).

If two functions are O(g), then so is their sum.

a is of order b exactly when a and b are equal. a is O(b) exactly when a a is (b) exactly when a>b.

If f and g are functions defined for all positive real numbers and if limx|f(x)g(x)|=C where C is a positive constant, then f is of order g.

If p is a polynomial of degree n, and q is a polynomial of degree m, and n

There is a "largest order", i.e. there is some function g so that all other functions f are O(g).

If two functions are of order g, then so is their sum.

The triangle inequality says that for all real numbers a and b, |a + b| |a| + |b|.

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