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# Solutions for Chapter 8.2: Manifolds and Integrals of k-forms ## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652 Solutions for Chapter 8.2: Manifolds and Integrals of k-forms

Solutions for Chapter 8.2
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##### 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. Chapter 8.2: Manifolds and Integrals of k-forms includes 15 full step-by-step solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Since 15 problems in chapter 8.2: Manifolds and Integrals of k-forms have been answered, more than 13491 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Algebraic expression

A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

• Arccosecant function

See Inverse cosecant function.

• Average velocity

The change in position divided by the change in time.

• Base

See Exponential function, Logarithmic function, nth power of a.

• Binomial coefficients

The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!

• Circular functions

Trigonometric functions when applied to real numbers are circular functions

• Degree of a polynomial (function)

The largest exponent on the variable in any of the terms of the polynomial (function)

• Differentiable at x = a

ƒ'(a) exists

• End behavior

The behavior of a graph of a function as.

• Exponential decay function

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

• Gaussian elimination

A method of solving a system of n linear equations in n unknowns.

• Higher-degree polynomial function

A polynomial function whose degree is ? 3

• Horizontal asymptote

The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

• Inverse sine function

The function y = sin-1 x

• Parametric equations for a line in space

The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

• Product of complex numbers

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

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

• Reference triangle

For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the x-axis, and a perpendicular dropped from a point on the terminal side to the x-axis. The angle in a reference triangle at the origin is the reference angle

• RRAM

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

• yz-plane

The points (0, y, z) in Cartesian space.

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