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# Solutions for Chapter 12: Vector-Valued Functions ## Full solutions for Calculus | 8th Edition

ISBN: 9780618502981 Solutions for Chapter 12: Vector-Valued Functions

Solutions for Chapter 12
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##### ISBN: 9780618502981

This textbook survival guide was created for the textbook: Calculus, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Since 90 problems in chapter 12: Vector-Valued Functions have been answered, more than 78786 students have viewed full step-by-step solutions from this chapter. Chapter 12: Vector-Valued Functions includes 90 full step-by-step solutions. Calculus was written by and is associated to the ISBN: 9780618502981.

Key Calculus Terms and definitions covered in this textbook
• Dependent event

An event whose probability depends on another event already occurring

• Discriminant

For the equation ax 2 + bx + c, the expression b2 - 4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2 - 4AC

• Divergence

A sequence or series diverges if it does not converge

• Double inequality

A statement that describes a bounded interval, such as 3 ? x < 5

• Elimination method

A method of solving a system of linear equations

• Equivalent systems of equations

Systems of equations that have the same solution.

• Explicitly defined sequence

A sequence in which the kth term is given as a function of k.

• Exponential decay function

Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

• Factor

In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

• Fitting a line or curve to data

Finding a line or curve that comes close to passing through all the points in a scatter plot.

• Linear regression line

The line for which the sum of the squares of the residuals is the smallest possible

• Magnitude of a real number

See Absolute value of a real number

The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

• Reciprocal of a real number

See Multiplicative inverse of a real number.

• Slant asymptote

An end behavior asymptote that is a slant line

• Slope

Ratio change in y/change in x

• Standard form of a polar equation of a conic

r = ke 1 e cos ? or r = ke 1 e sin ? ,

• Triangular form

A special form for a system of linear equations that facilitates finding the solution.

• Unit vector

Vector of length 1.

• Vertex of a parabola

The point of intersection of a parabola and its line of symmetry.

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