- 4.R.1E: What can be said about the extreme values of a function that is con...
- 4.R.2E: What does it mean for a function to have a local extreme value on i...
- 4.R.3E: How do you find the absolute extrema of a continuous function on a ...
- 4.R.4E: What are the hypotheses and conclusion of Rolle’s Theorem? Are the ...
- 4.R.5E: What are the hypotheses and conclusion of the Mean Value Theorem? W...
- 4.R.6E: State the Mean Value Theorem’s three corollaries.
- 4.R.7E: How can you sometimes identify a function ƒ(x) by knowing f’ and kn...
- 4.R.8E: What is the First Derivative Test for Local Extreme Values? Give ex...
- 4.R.9E: How do you test a twice-differentiable function to determine where ...
- 4.R.10E: What is an inflection point? Give an example. What physical signifi...
- 4.R.11E: What is the Second Derivative Test for Local Extreme Values? Give e...
- 4.R.12E: What do the derivatives of a function tell you about the shape of i...
- 4.R.13E: List the steps you would take to graph a polynomial function. Illus...
- 4.R.14E: What is a cusp? Give examples.
- 4.R.15E: List the steps you would take to graph a rational function. Illustr...
- 4.R.16E: Outline a general strategy for solving max-min problems. Give examp...
- 4.R.17E: Describe l’Hôpital’s Rule. How do you know when to use the rule and...
- 4.R.18E: How can you sometimes handle limits that lead to indeterminate form...
- 4.R.19E: How can you sometimes handle limits that lead to indeterminate form...
- 4.R.20E: Describe Newton’s method for solving equations. Give an example. Wh...
- 4.R.21E: Can a function have more than one antiderivative? If so, how are th...
- 4.R.22E: What is an indefinite integral? How do you evaluate one? What gener...
- 4.R.23E: How can you sometimes solve a differential equation of the form dy/...
- 4.R.24E: What is an initial value problem? How do you solve one? Give an exa...
- 4.R.25E: If you know the acceleration of a body moving along a coordinate li...
Solutions for Chapter 4.R: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals | 2nd Edition
The farthest point from the Sun in a planet’s orbit
Measure of the clockwise angle that the line of travel makes with due north
nth root, where n = 3 (see Principal nth root),
Distance (on a number line)
The distance between real numbers a and b, or |a - b|
equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)
Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.
A series whose terms form a geometric sequence.
Identity involving a trigonometric function of u/2.
Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0
Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible
Measure of center
A measure of the typical, middle, or average value for a data set
Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b
Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.
The principle of experimental design that makes it possible to use the laws of probability when making inferences.
Numbers that can be written as a/b, where a and b are integers, and b ? 0.
See Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the x-axis, and a perpendicular dropped from a point on the terminal side to the x-axis. The angle in a reference triangle at the origin is the reference angle
The numbers 0, 1, 2, 3, ... .