- 1.1.1: In Exercises 1-4, decide whetlier ttie problem can be solved using ...
- 1.1.2: In Exercises 1-4, decide whetlier ttie problem can be solved using ...
- 1.1.3: In Exercises 1-4, decide whetlier ttie problem can be solved using ...
- 1.1.4: In Exercises 1-4, decide whetlier ttie problem can be solved using ...
- 1.1.5: In Exercises 5 and 6, find the area of the shaded region.
- 1.1.6: In Exercises 5 and 6, find the area of the shaded region.
- 1.1.7: In Exercises 7 and 8, find the volume of the solid shown.
- 1.1.8: In Exercises 7 and 8, find the volume of the solid shown.
- 1.1.9: (a) Use the list feature of a graphing utility to graph the followi...
- 1.1.10: la) (Note: If you cannot use lists on your graphing utMity, graph V...
- 1.1.11: Consider the length of the graph of fix) = 5/.v from (1.5) to (5, I...
Solutions for Chapter 1.1: A Preview of Calculus
Full solutions for Calculus of A Single Variable | 7th Edition
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.
Absolute value of a real number
Denoted by |a|, represents the number a or the positive number -a if a < 0.
An equation that relates variable quantities associated with phenomena being studied
Characteristic polynomial of a square matrix A
det(xIn - A), where A is an n x n matrix
Extracting square roots
A method for solving equations in the form x 2 = k.
Frequency (in statistics)
The number of individuals or observations with a certain characteristic.
Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
An equation written with logarithms instead of exponents
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior
Any of the real numbers in a matrix
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.
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.
A variable that is affected by an explanatory variable.
A transformation that leaves the basic shape of a graph unchanged.
A plot of all the ordered pairs of a two-variable data set on a coordinate plane.
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.
Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.