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# Solutions for Chapter 2.5: The Chain Rule ## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652 Solutions for Chapter 2.5: The Chain Rule

Solutions for Chapter 2.5
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##### ISBN: 9780321780652

Chapter 2.5: The Chain Rule includes 45 full step-by-step solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Since 45 problems in chapter 2.5: The Chain Rule have been answered, more than 12722 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Acute angle

An angle whose measure is between 0° and 90°

• Angle

Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

• Augmented matrix

A matrix that represents a system of equations.

• Future value of an annuity

The net amount of money returned from an annuity.

• Horizontal component

See Component form of a vector.

• Horizontal line

y = b.

• LRAM

A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand endpoint of each subinterval

• Modified boxplot

A boxplot with the outliers removed.

• Parabola

The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

• Probability of an event in a finite sample space of equally likely outcomes

The number of outcomes in the event divided by the number of outcomes in the sample space.

• Pythagorean identities

sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

• Reflection across the x-axis

x, y and (x,-y) are reflections of each other across the x-axis.

• Repeated zeros

Zeros of multiplicity ? 2 (see Multiplicity).

• Rose curve

A graph of a polar equation or r = a cos nu.

• Sequence of partial sums

The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

• Standard unit vectors

In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

• Sum identity

An identity involving a trigonometric function of u + v

• Upper bound for ƒ

Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

• Vertical line test

A test for determining whether a graph is a function.

• y-axis

Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.

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