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Chapter 10: Q.0 (page 777)

Read the section and make your own summary of the material.

Short Answer

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The area under a curve, sigma notation and limits of sums can be reviewed

Step by step solution

01

Step 1. Summary

  • Sigma Notation and Properties of sum.
  • Limits of sum, and definition of definite integral.

A study of the accumulation function.

  • The accumulation function A(x) gives the accumulation of area between the horizontal axis and the graph f(x) between 0 to x.

A(x)=∫0x f(x)dx

02

Step 2. Continue

  • Sigma Notation and Properties of sum.

∑k=starting_valueending_value (function_of_k)1.∑k=1n ak+bk=∑k=1n ak+∑k=1n bk2.∑k=1n ak=∑k=1p−1 ak+∑k=pn ak

  • Calculating sums of areas of small rectangles using definite integral.

∫0x f(x)dx=limn→∞ ∑k=1n fckΔxΔx=b−anck=a+kΔx

Thus, the area under a curve, sigma notation and limits of sums can be reviewed.

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Most popular questions from this chapter

Suppose that we know the reciprocal rule for limits: If limx→cg(x)=Mexists and is nonzero, then limx→c1g(x)=1MThis limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.

In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)

role="math" localid="1649400253452" (u×v)×wandu×(v×w)

In Exercises 24-27, find compuv,projuvand the component of v orthogonal tou.

u=3,-1,2,v=-4,-6,3

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(4,3,−2),Q(0,0,3),R(−1,3,6)

What is meant by the parallelogram determined by vectors u and v in ℝ3? How do you find the area of this parallelogram?
See all solutions

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