- 6.27P: A satellite orbiting the moon very near the surface has a period of...
- 6.28MCQ: Currently, the moon goes around the earth once every 27.3 days. If ...
- 6.28P: The centers of a 10 kg lead ball and a 100 g lead ball are separate...
- 6.29MCQ: Two planets orbit a star. You can ignore the gravitational interact...
- 6.29P: The gravitational force of a star on an orbiting planet?1 is ?F1 Pl...
- 6.30MCQ: A particle undergoing circular motion in t? he x ? y-plane stops on...
- 6.30P: The free-fall acceleration at the surface of planet 1 is . The radi...
- 6.31MCQ: Questions concern a classic figure-skating jump called the axle. A ...
- 6.87AE: AE Do removable discontinuities exist? a. Does the fu ? n?cti? ?? )...
Solutions for Chapter 6: Derivatives
Full solutions for Calculus: Early Transcendentals | 1st Edition
Summary of Chapter 6: Derivatives
We use limits not only to define the derivative but also to develop efficient rules for finding derivatives. The applications of the derivative—which we introduce along the way—are endless because almost everything around us is in a state of change, and derivatives describe change.
Directed line segment
Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1 - x 2)2 + (y1 - y2)2
Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2
equation of a hyperbola
(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1
Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.
Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.
See Component form of a vector.
a + 0 = a, a ? 1 = a
Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.
Angle generated by a counterclockwise rotation.
Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.
The function y = sin x.
Symmetric about the y-axis
A graph in which (-x, y) is on the graph whenever (x, y) is; or a graph in which (-r, -?) or (r, ?, -?) is on the graph whenever (r, ?) is
Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).
Variable (in statistics)
A characteristic of individuals that is being identified or measured.
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.
A point that lies on both the graph and the y-axis.