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# Solutions for Chapter 9: Polar Coordinates and Parametric Curves

## Full solutions for Calculus:Early Transcendentals | 7th Edition

ISBN: 9780131569898

Solutions for Chapter 9: Polar Coordinates and Parametric Curves

Solutions for Chapter 9
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##### ISBN: 9780131569898

Summary of Chapter 9: Polar Coordinates and Parametric Curves

The use of parametric equations and polar coordinates allows for the analysis of families of curves difficult to handle through rectangular coordinates. Using polar coordinates, curves with loops can appear as graphs of functions. Parabola, ellipes, and hyperbola as plane sections of a cone. Polar coordinates in the plane

This expansive textbook survival guide covers the following chapters and their solutions. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Chapter 9: Polar Coordinates and Parametric Curves includes 83 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7. Since 83 problems in chapter 9: Polar Coordinates and Parametric Curves have been answered, more than 40425 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Arccotangent function

See Inverse cotangent function.

• Basic logistic function

The function ƒ(x) = 1 / 1 + e-x

• Combination

An arrangement of elements of a set, in which order is not important

• Direction vector for a line

A vector in the direction of a line in three-dimensional space

• Distance (in Cartesian space)

The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x ) - x 2)2 + (y1 - y2)2 + (z 1 - z 2)2

• equation of a quadratic function

ƒ(x) = ax 2 + bx + c(a ? 0)

• Equilibrium point

A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

• Extracting square roots

A method for solving equations in the form x 2 = k.

• Future value of an annuity

The net amount of money returned from an annuity.

• Inverse tangent function

The function y = tan-1 x

• Monomial function

A polynomial with exactly one term.

• NDER ƒ(a)

See Numerical derivative of ƒ at x = a.

• Polar coordinate system

A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

• Polynomial in x

An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

• Solution of a system in two variables

An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

• Square matrix

A matrix whose number of rows equals the number of columns.

• Symmetric difference quotient of ƒ at a

ƒ(x + h) - ƒ(x - h) 2h

• Zero factorial

See n factorial.

• Zero of a function

A value in the domain of a function that makes the function value zero.