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Properties of Dot Product
u→ • (v→ + w→) = u→ • v→ + u→ • w→ (cv→) • w→ = v→ •(cw→) = c (v→•w→)
v→ • w→ = w→ • v→ v→ • 0→ = 0
v→ • v→ = ||v→||2 if v→•v→ = 0 then v→ = 0→
1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y). (a) Prove that R is an equivalence relation on Z. (b) If for every x ? Z, the equivalenc
1.A=the set of whole numbers less tan 4 ? 2.B=the set of prime numbers less than 19 ? 3.C=the set of first three days of week?
In the earlier section we introduced the Wronskian to assist us find out whether two solutions were a fundamental set of solutions. Under this section we will look at the other app
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Velocity : Recall that it can be thought of as special case of the rate of change interpretation. If the situation of an object is specified by f(t ) after t units of time the vel
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
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The index of industrial production This is a quantity index compiled by the government. This measures changes in the volume of production in main industries. The index is a ex
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