 68.1: The derivative of a function at a point is its instantaneous rate o...
 68.2: A definite integral is a product of x and y, where y is allowed to ...
 68.3: Derivatives and definite integrals are defined precisely by using t...
 68.4: Intuitively, a limit is a yvalue that f(x) stays close to when x i...
 68.5: Limits are the basis for the formal definition of derivative. Write...
 68.6: Show that you can operate with the definition of derivative by usin...
 68.7: Properties such as the one used in allow you to calculate derivativ...
 68.8: When composite functions are involved, you must remember the chain ...
 68.9: Derivatives can be interpreted graphically. Show that you understan...
 68.10: Youve learned to differentiate products and quotients, and to find ...
 68.11: Piecewise functions can sometimes be differentiable at a point wher...
 68.12: Definite integrals can be calculated numerically by using Riemann s...
 68.13: The definition of definite integral involves the limit of a Riemann...
 68.14: Indefinite integrals are antiderivatives. Evaluate: a. cos5 x sin x...
 68.15: The fundamental theorem of calculus gives an algebraic way to calcu...
 68.16: The fundamental theorem is proved using the mean value theorem as a...
 68.17: Much of calculus involves learning how to work problems algebraical...
 68.18: Explain why the power rule for derivatives never gives x1 as the an...
 68.19: The fundamental theorem in its other form lets you take the derivat...
 68.20: Show how the fundamental theorem in its second form lets you write ...
 68.21: The function you should have written in is the natural logarithm fu...
 68.22: Using the parametric chain rule, you can find dy/dx for functions s...
 68.23: The ellipse in Figure 68c has the parametric equations given in 22...
 68.24: You can apply derivatives to realworld problems. Suppose that a ca...
 68.25: Derivatives can also be applied to problems from the mathematical w...
 68.26: In the differentiation of the baseb logarithm function, this limit...
 68.27: You can use derivatives to find related rates of moving objects. Fi...
 68.28: Simpsons rule can be used to find definite integrals numerically if...
 68.29: You can use integrals to find the volume of a solid object that has...
 68.30: It is important for you to be able to write about mathematics. Has ...
Solutions for Chapter 68: Cumulative Review: Chapters 16
Full solutions for Calculus: Concepts and Applications  2nd Edition
ISBN: 9781559536547
Solutions for Chapter 68: Cumulative Review: Chapters 16
Get Full SolutionsChapter 68: Cumulative Review: Chapters 16 includes 30 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 30 problems in chapter 68: Cumulative Review: Chapters 16 have been answered, more than 20970 students have viewed full stepbystep solutions from this chapter. Calculus: Concepts and Applications was written by and is associated to the ISBN: 9781559536547. This textbook survival guide was created for the textbook: Calculus: Concepts and Applications, edition: 2.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Anchor
See Mathematical induction.

Binomial theorem
A theorem that gives an expansion formula for (a + b)n

Center
The central point in a circle, ellipse, hyperbola, or sphere

Compounded monthly
See Compounded k times per year.

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Demand curve
p = g(x), where x represents demand and p represents price

Horizontal line
y = b.

Inequality symbol or
<,>,<,>.

Leading coefficient
See Polynomial function in x

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

Positive angle
Angle generated by a counterclockwise rotation.

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Quadratic function
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.

Rectangular coordinate system
See Cartesian coordinate system.

Relation
A set of ordered pairs of real numbers.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Spiral of Archimedes
The graph of the polar curve.

Union of two sets A and B
The set of all elements that belong to A or B or both.