- 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
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 z-components 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)
An identity involving a trigonometric function of u - v
Difference of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
See Mathematical induction.
Point where a curve crosses the x-, y-, or z-axis 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)
The formula x = -b 2b2 - 4ac2a used to solve ax 2 + bx + c = 0.
A procedure for fitting a quartic function to a set of data.
A function that assigns real-number values to the outcomes in a sample space.
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>.
The numbers 0, 1, 2, 3, ... .
Zero of a function
A value in the domain of a function that makes the function value zero.