 14.10.1E: Finding Partial Derivatives with Constrained VariablesIn Exercise, ...
 14.10.2E: Finding Partial Derivatives with Constrained VariablesIn Exercise, ...
 14.10.3E: Finding Partial Derivatives with Constrained VariablesIn Exercise, ...
 14.10.4E: Finding Partial Derivatives with Constrained VariablesFind
 14.10.5E: Finding Partial Derivatives with Constrained VariablesFind
 14.10.6E: Finding Partial Derivatives with Constrained VariablesFind and y = uv.
 14.10.7E: Finding Partial Derivatives with Constrained VariablesSuppose that ...
 14.10.8E: Finding Partial Derivatives with Constrained VariablesSuppose that ...
 14.10.9E: Theory and ExamplesEstablish the fact, widely used in hydrodynamics...
 14.10.10E: Theory and ExamplesIf z = x + ƒ(u),where u = xy show that
 14.10.11E: Theory and ExamplesSuppose that the equation g(x, y, z) = 0 determi...
 14.10.12E: Theory and ExamplesSuppose that ƒ(x, y, z, w) = 0 and g(x, y, z, w)...
Solutions for Chapter 14.10: Thomas' Calculus: Early Transcendentals 13th Edition
Full solutions for Thomas' Calculus: Early Transcendentals  13th Edition
ISBN: 9780321884077
Solutions for Chapter 14.10
Get Full SolutionsThis textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. Chapter 14.10 includes 12 full stepbystep solutions. Since 12 problems in chapter 14.10 have been answered, more than 82430 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Difference identity
An identity involving a trigonometric function of u  v

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Inductive step
See Mathematical induction.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Present value of an annuity T
he net amount of your money put into an annuity.

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Quartic regression
A procedure for fitting a quartic function to a set of data.

Random variable
A function that assigns realnumber values to the outcomes in a sample space.

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Sum of an infinite series
See Convergence of a series

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

Whole numbers
The numbers 0, 1, 2, 3, ... .

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