- 6.AAE.1AAE: A solid is generated by revolving about the x-axis the region bound...
- 6.AAE.2AAE: A solid is generated by revolving about the x-axis the region bound...
- 6.AAE.3AAE: Suppose that the increasing function ƒ(x) is smooth for x ? 0 and t...
- 6.AAE.4AAE: a. Show that for b. Generalize the result in part (a).
- 6.AAE.5AAE: Find the volume of the solid formed by revolving the region bounded...
- 6.AAE.6AAE: Consider a right-circular cylinder of diameter 1. Form a wedge by m...
- 6.AAE.7AAE: At points on the curve line segments of length h=y are drawn perpen...
- 6.AAE.8AAE: At points on a circle of radius a, line segments are drawn perpendi...
- 6.AAE.9AAE: A particle of mass m starts from rest at time t=0 and is moved alon...
- 6.AAE.10AAE: Work and kinetic energy Suppose a 1.6-oz golf ball is placed on a v...
- 6.AAE.11AAE: Find the centroid of the region bounded below by the x-axis and abo...
- 6.AAE.12AAE: If you haul a telephone pole on a two-wheeled carriage behind a tru...
- 6.AAE.13AAE: Suppose that a thin metal plate of area A and constant density occu...
- 6.AAE.14AAE: Find the center of mass of a thin plate covering the region bounded...
- 6.AAE.15AAE: a. Find the centroid of the region in the first quadrant bounded by...
- 6.AAE.16AAE: A triangular corner is cut from a square 1 ft on a side. The area o...
Solutions for Chapter 6.AAE: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals | 2nd Edition
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once
Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data
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)
A sequence or series diverges if it does not converge
See Equilibrium point.
Horizontal Line Test
A test for determining whether the inverse of a relation is a function.
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
A function whose domain is the set of all natural numbers.
Integrable over [a, b] Lba
ƒ1x2 dx exists.
Connected subset of the real number line with at least two points, p. 4.
The notation dy/dx for the derivative of ƒ.
An equation written with logarithms instead of exponents
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.
Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.
The function y = sin x.
Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i
An interval that extends to -? or ? (or both).
Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.
Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.
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>.