 12.5.1: is a constant
 12.5.2: n i1 c i n
 12.5.3: n i1 i 3 n i
 12.5.4: The exact _______ of a plane region is the limit of the sum of rect...
 12.5.5: 60 i1 7
 12.5.6: 45 i1 3 6
 12.5.7: 20 i1 i 3
 12.5.8: 30 i1 i 2
 12.5.9: 20 k1 k3 2
 12.5.10: 50 k1 2k 1 20
 12.5.11: 25 j1 j 2 j 5
 12.5.12: 10 j1 j 3 3j 2 25
 12.5.13: n i1 i 3 n4
 12.5.14: n i1 i n 2 n
 12.5.15: n i1 3 n31 i 2
 12.5.16: n i1 2i 3 n 2 n
 12.5.17: n i1 i 2 n3 2 n1 n
 12.5.18: n i1 3 2 i n 1 n n
 12.5.19: n i1 1 i n 2 1 n
 12.5.20: i1 4 n 2i n2 2i n n
 12.5.21: fx x 4
 12.5.22: fx 2 x2 fx
 12.5.23: fx 1 4x3
 12.5.24: fx 1 2x 13 fx
 12.5.25: fx x 1 1 3x 4 n 4
 12.5.26: fx 3 2 fx x 1 1 3x
 12.5.27: fx 9 x 2 1 2 x
 12.5.28: fx x fx 9 x 2 1 2 x
 12.5.29: fx 1 9x3 x
 12.5.30: fx 3 1 4x3 fx
 12.5.31: fx 2x 5 0, 4 n
 12.5.32: fx 20 2x 2, 6 f
 12.5.33: fx 9 x 0, 2 2
 12.5.34: fx x 4, 6 2
 12.5.35: fx 1, 3 1 2 x 4 fx
 12.5.36: fx 2, 2 1 2 x 1 fx
 12.5.37: fx 4x 1 0, 1 x
 12.5.38: fx 3x 2 0, 2 fx
 12.5.39: fx 2x 3 0, 1 fx
 12.5.40: fx 3x 4 2, 5
 12.5.41: fx 2 x 1, 1 2
 12.5.42: fx x 0, 1 2
 12.5.43: gx 8 x 1, 2 3
 12.5.44: gx 4x x 0, 2 3
 12.5.45: fx 1, 4 1
 12.5.46: fx x 1, 1 2
 12.5.47: Civil Engineering The boundaries of a parcel of land are two edges ...
 12.5.48: Civil Engineering The table shows the measurements (in feet) of a l...
 12.5.49: Writing Write a paragraph describing the process of finding the are...
 12.5.50: HOW DO YOU SEE IT? Determine which value best approximates the area...
 12.5.51: The sum of the first positive integers is
 12.5.52: The exact area of a plane region is the limit of the sum of rectang...
Solutions for Chapter 12.5: The Area Problem
Full solutions for Precalculus with Limits  3rd Edition
ISBN: 9781133947202
Solutions for Chapter 12.5: The Area Problem
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus with Limits, edition: 3. Since 52 problems in chapter 12.5: The Area Problem have been answered, more than 35738 students have viewed full stepbystep solutions from this chapter. Chapter 12.5: The Area Problem includes 52 full stepbystep solutions. Precalculus with Limits was written by and is associated to the ISBN: 9781133947202.

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Bar chart
A rectangular graphical display of categorical data.

Composition of functions
(f ? g) (x) = f (g(x))

Identity
An equation that is always true throughout its domain.

Implied domain
The domain of a function’s algebraic expression.

Multiplicative inverse of a matrix
See Inverse of a matrix

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Perpendicular lines
Two lines that are at right angles to each other

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Real axis
See Complex plane.

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Root of a number
See Principal nth root.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Solve by elimination or substitution
Methods for solving systems of linear equations.

Subtraction
a  b = a + (b)

Time plot
A line graph in which time is measured on the horizontal axis.

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

xintercept
A point that lies on both the graph and the xaxis,.