- 16.1: A vector ield F, a curve C, and a point P are shown. (a) Is yC F dr...
- 16.2: Evaluate the line integral
- 16.3: Evaluate the line integral
- 16.4: Evaluate the line integral
- 16.5: Evaluate the line integral
- 16.6: Evaluate the line integral
- 16.7: Evaluate the line integral
- 16.8: Evaluate the line integral
- 16.9: Evaluate the line integral
- 16.10: Find the work done by the force ield Fsx, y, zd z i 1 x j 1 y k in ...
- 16.11: Show that F is a conservative vector ield. Then ind a function f su...
- 16.12: Show that F is a conservative vector ield. Then ind a function f su...
- 16.13: Show that F is conservative and use this fact to evaluate yC F dr a...
- 16.14: Show that F is conservative and use this fact to evaluate yC F dr a...
- 16.15: Verify that Greens Theorem is true for the line integral yC xy 2 dx...
- 16.16: Use Greens Theorem to evaluate y C s1 1 x 3 dx 1 2xy dy where C is ...
- 16.17: Use Greens Theorem to evaluate yC x 2 y dx 2 xy 2 dy, where C is th...
- 16.18: Find curl F and div F if Fsx, y, zd e 2x sin y i 1 e 2y sin z j 1 e...
- 16.19: Show that there is no vector ield G such that curl G 2x i 1 3yz j 2...
- 16.20: If F and G are vector ields whose component functions have continuo...
- 16.21: If C is any piecewise-smooth simple closed plane curve and f and t ...
- 16.22: If f and t are twice differentiable functions, show that = 2 s ftd ...
- 16.23: If f is a harmonic function, that is, = 2 f 0, show that the line i...
- 16.24: (a) Sketch the curve C with parametric equations x cos t y sin t z ...
- 16.25: Find the area of the part of the surface z x 2 1 2y that lies above...
- 16.26: (a) Find an equation of the tangent plane at the point s4, 22, 1d t...
- 16.27: Evaluate the surface integral.
- 16.28: Evaluate the surface integral.
- 16.29: Evaluate the surface integral.
- 16.30: Evaluate the surface integral.
- 16.31: Verify that Stokes Theorem is true for the vector ield Fsx, y, zd x...
- 16.32: Use Stokes Theorem to evaluate yyS curl F dS, where Fsx, y, zd x 2 ...
- 16.33: Use Stokes Theorem to evaluate yC F dr, where Fsx, y, zd xy i 1 yz ...
- 16.34: Use the Divergence Theorem to calculate the surface integral yyS F ...
- 16.35: Verify that the Divergence Theorem is true for the vector ield Fsx,...
- 16.36: Compute the outward lux of Fsx, y, zd x i 1 y j 1 z k sx 2 1 y 2 1 ...
- 16.37: Let Fsx, y, zd s3x 2 yz 2 3yd i 1 sx 3 z 2 3xd j 1 sx 3 y 1 2zd k E...
- 16.38: Let Fsx, yd s2x 3 1 2xy 2 2 2yd i 1 s2y 3 1 2x 2 y 1 2xd j x 2 1 y ...
- 16.39: Find yyS F n dS, where Fsx, y, zd x i 1 y j 1 z k and S is the outw...
- 16.40: If the components of F have continuous second partial derivatives a...
- 16.41: If a is a constant vector, r x i 1 y j 1 z k, and S is an oriented,...
Solutions for Chapter 16: Calculus: Early Transcendentals 8th Edition
Full solutions for Calculus: Early Transcendentals | 8th Edition
a + (b + c) = (a + b) + c, a(bc) = (ab)c.
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined
Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)
a b = aa 1 b b, b Z 0
Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2
Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.
Variable representing the domain value of a function (usually x).
Any of the real numbers in a matrix
Multiplication principle of counting
A principle used to find the number of ways an event can occur.
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).
Real part of a complex number
See Complex number.
The function ƒ(x) = 1x
Reciprocal of a real number
See Multiplicative inverse of a real number.
See Division algorithm for polynomials.
Angle measure equal to 1/60 of a minute.
Second-degree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically
Vertical line test
A test for determining whether a graph is a function.
The function that associates points on the unit circle with points on the real number line