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# Solutions for Chapter 1.2: Physical Applications

## Full solutions for Calculus: Early Transcendentals | 1st Edition

ISBN: 9780321570567

Solutions for Chapter 1.2: Physical Applications

Solutions for Chapter 1.2
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##### ISBN: 9780321570567

Summary of Chapter 1.2: Physical Applications

A surface area problem is “between” a volume problem (which is threedimensional) and an arc length problem (which is one-dimensional)

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Chapter 1.2: Physical Applications includes 67 full step-by-step solutions. Since 67 problems in chapter 1.2: Physical Applications have been answered, more than 430500 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Bounded

A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

• Cone

See Right circular cone.

• Constraints

See Linear programming problem.

• Ellipse

The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

• Head minus tail (HMT) rule

An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2 - x 1, y2 - y19>

• Initial value of a function

ƒ 0.

• Integers

The numbers . . ., -3, -2, -1, 0,1,2,...2

• Inverse secant function

The function y = sec-1 x

• Lemniscate

A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

• Linear inequality in two variables x and y

An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

• Logistic growth function

A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth

• Magnitude of an arrow

The magnitude of PQ is the distance between P and Q

• Matrix, m x n

A rectangular array of m rows and n columns of real numbers

• Multiplication property of equality

If u = v and w = z, then uw = vz

• Opposite

See Additive inverse of a real number and Additive inverse of a complex number.

• Perihelion

The closest point to the Sun in a planet’s orbit.

• 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.

• Proportional

See Power function

• Solve by substitution

Method for solving systems of linear equations.

• Sum of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i