 13.1: A vector field , a curve , and a point are shown. (a) Is positive, ...
 13.2: Evaluate the line integral.is the arc of the parabola from
 13.3: Evaluate the line integral.xC yz cos x ds C x t y 3 cos t z 3 sin t...
 13.4: Evaluate the line integral.is the ellipse with counterclockwise ori...
 13.5: Evaluate the line integral.xC y C
 13.6: Evaluate the line integral.xC sxy dx e y dy xz dz C rt t 4 i t 2 j ...
 13.7: Evaluate the line integral.xC xy dx y 2 dy yz dz C 1, 0, 1 3, 4, 2 ...
 13.8: Evaluate the line integral.xC F dr Fx, y x y i x 2 j C rt sin t i 1...
 13.9: Evaluate the line integral.xC F dr Fx, y, z ez i xz j x y k C rt t ...
 13.10: Find the work done by the force field in moving a particle from the...
 13.11: Show that is a conservative vector field. Then find a function such...
 13.12: Show that is a conservative vector field. Then find a function such...
 13.13: Show that is conservative and use this fact to evaluate along the g...
 13.14: Show that is conservative and use this fact to evaluate along the g...
 13.15: Verify that Greens Theorem is true for the line integral , where co...
 13.16: Use Greens Theorem to evaluate where is the triangle with vertices
 13.17: Use Greens Theorem to evaluate , where is the circle with countercl...
 13.18: Find curl and div if
 13.19: Show that there is no vector field such tha
 13.20: Show that, under conditions to be stated on the vector fields and ,...
 13.21: If is any piecewisesmooth simple closed plane curve and and are di...
 13.22: If and are twice differentiable functions, show that
 13.23: If is a harmonic function, that is, , show that the line integral i...
 13.24: (a) Sketch the curve with parametric equations (b) Find xC 2xe 2y d...
 13.25: Find the area of the part of the surface that lies above the triang...
 13.26: (a) Find an equation of the tangent plane at the point to the param...
 13.27: Evaluate the surface integral.
 13.28: Evaluate the surface integral.
 13.29: Evaluate the surface integral.
 13.30: Evaluate the surface integral.
 13.31: Verify that Stokes Theorem is true for the vector field , where is ...
 13.32: Use Stokes Theorem to evaluate , where , is the part of the sphere ...
 13.33: Use Stokes Theorem to evaluate , where , and is the triangle with v...
 13.34: Use the Divergence Theorem to calculate the surface integral , wher...
 13.35: Verify that the Divergence Theorem is true for the vector field , w...
 13.36: Compute the outward flux of through the ellipsoid
 13.37: Find , where and is the outwardly oriented surface shown in the fig...
 13.38: Let Evaluate , where is shown in the figure.
 13.39: If is a constant vector, , and is an oriented, smooth surface with ...
 13.40: If the components of have continuous second partial derivatives and...
Solutions for Chapter 13: Essential Calculus 2nd Edition
Full solutions for Essential Calculus  2nd Edition
ISBN: 9781133112297
Solutions for Chapter 13
Get Full SolutionsChapter 13 includes 40 full stepbystep solutions. Essential Calculus was written by and is associated to the ISBN: 9781133112297. Since 40 problems in chapter 13 have been answered, more than 5201 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Essential Calculus, edition: 2.

Distributive property
a(b + c) = ab + ac and related properties

Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Halfangle identity
Identity involving a trigonometric function of u/2.

Hypotenuse
Side opposite the right angle in a right triangle.

Instantaneous rate of change
See Derivative at x = a.

Inverse cosine function
The function y = cos1 x

Inverse cotangent function
The function y = cot1 x

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Linear regression equation
Equation of a linear regression line

Quartic function
A degree 4 polynomial function.

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

Real number line
A horizontal line that represents the set of real numbers.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Right angle
A 90° angle.

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

Slope
Ratio change in y/change in x

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

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

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.