- 4.4.1: Find the line that best fits the following data: (0, 2), (1, 3), (2...
- 4.4.2: Show that if you have only two data points (x1, y1) and (x2, y2), t...
- 4.4.3: Suppose that you are given n pairs of data (x1, y1), (x2, y2),...,(...
- 4.4.4: Find the curve of the form y = a/x + b that best fits the following...
- 4.4.5: Suppose that you have n pairs of data (x1, y1), (x2, y2),..., (xn, ...
- 4.4.6: (Note: This exercise will be facilitated by the use of a spreadshee...
- 4.4.7: Let F = (2x 2y 1)i + (2x 6y 2)j. (a) Show that F is conservative an...
- 4.4.8: Suppose a particle moves in a vector field F in R2 with physical po...
- 4.4.9: Let a particle move in the vector field F in R3 whose physical pote...
- 4.4.10: Suppose that a particle of mass m is constrained to move on the ell...
- 4.4.11: The Sukolux Vacuum Cleaner Company manufactures and sells three typ...
- 4.4.12: Some simple electronic devices are to be designed to include three ...
- 4.4.13: A farmer has determined that her cornfield will yield corn (in bush...
- 4.4.14: A farmer has determined that her cornfield will yield corn (in bush...
- 4.4.15: The CEO of the Wild Widget Company has decided to invest $360,000 i...
- 4.4.16: Let Q(K, L) be a production function for a company where K and L re...
Solutions for Chapter 4.4: Some Applications of Extrema
Full solutions for Vector Calculus | 4th Edition
An experiment in which subjects do not know if they have been given an active treatment or a placebo
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.
An arrangement of elements of a set, in which order is not important
See Geometric sequence.
De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)
A sequence or series diverges if it does not converge
Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.
See Power function.
Matrix, m x n
A rectangular array of m rows and n columns of real numbers
See Principal nth root
Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002
A triangle in which one angle is greater than 90°.
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.
Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22 - 2r1r2 cos 1?1 - ?22
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.
Zeros of a function that are rational numbers.
A 90° angle.
Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.
Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system
Terms of a sequence
The range elements of a sequence.