- 2.1.1: Find the distance traveled in 15 seconds by an object traveling at ...
- 2.1.2: Find the distance traveled in 15 seconds by an object moving with a...
- 2.1.3: Rate of Change A bicyclist is riding on a path modeled by the funct...
- 2.1.4: A bicyclist is riding on a path modeled by the function where and a...
- 2.1.5: Find the area of the shaded region. (a) (b)
- 2.1.6: Secant Lines Consider the function and the point on the graph of (a...
- 2.1.7: Secant Lines Consider the function and the point on the graph of (a...
- 2.1.8: HOW DO YOU SEE IT? How would you describe the instantaneous rate of...
- 2.1.9: Approximating Area Use the rectangles in each graph to approximate ...
- 2.1.10: Approximating the Length of a Curve Consider the length of the grap...
Solutions for Chapter 2.1: A Preview of Calculus
Full solutions for Calculus: Early Transcendental Functions | 6th Edition
Composition of functions
(f ? g) (x) = f (g(x))
Directed line segment
The line through the focus and perpendicular to the directrix of a conic.
Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.
Integrable over [a, b] Lba
ƒ1x2 dx exists.
Inverse cosecant function
The function y = csc-1 x
Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.
Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible
Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.
Negative linear correlation
See Linear correlation.
Order of magnitude (of n)
If a polynomial f(x) is divided by x - c , the remainder is ƒ(c)
Resolving a vector
Finding the horizontal and vertical components of a vector.
Set of all possible outcomes of an experiment.
A process for gathering data from a subset of a population, usually through direct questioning.
The function y = sin x.
A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.
A measure of how a data set is spread
Stretch of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.
Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.