 5.1.1: (a) By reading values from the given graph of , use five rectangles...
 5.1.2: (a) Use six rectangles to find estimates of each type for the area ...
 5.1.3: (a) Estimate the area under the graph of from to using four approxi...
 5.1.4: (a) Estimate the area under the graph of from x 0 to using x 5 five...
 5.1.5: a) Estimate the area under the graph of from to using three rectang...
 5.1.6: (a) Graph the function . (b) Estimate the area under the graph of u...
 5.1.7: With a programmable calculator (or a computer), it is possible to e...
 5.1.8: With a programmable calculator (or a computer), it is possible to e...
 5.1.9: Some computer algebra systems have commands that will draw approxim...
 5.1.10: a) If , use the commands discussed in Exercise 9 to find the left a...
 5.1.11: The speed of a runner increased steadily during the first three sec...
 5.1.12: Speedometer readings for a motorcycle at 12second intervals are gi...
 5.1.13: Oil leaked from a tank at a rate of liters per hour. The rate decre...
 5.1.14: When we estimate distances from velocity data, it is sometimes nece...
 5.1.15: The velocity graph of a braking car is shown. Use it to estimate th...
 5.1.16: The velocity graph of a car accelerating from rest to a speed of ov...
 5.1.17: Use Definition 2 to find an expression for the area under the graph...
 5.1.18: Use Definition 2 to find an expression for the area under the graph...
 5.1.19: Use Definition 2 to find an expression for the area under the graph...
 5.1.20: Determine a region whose area is equal to the given limit. Do not e...
 5.1.21: Determine a region whose area is equal to the given limit. Do not e...
 5.1.22: (a) Use Definition 2 to find an expression for the area under the c...
 5.1.23: (a) Express the area under the curve from 0 to 2 as a CAS y cos x l...
 5.1.24: Find the exact area of the region under the graph of from 0 to 2 by...
 5.1.25: Find the exact area under the cosine curve from to , where . (Use a...
 5.1.26: (a) Let be the area of a polygon with equal sides inscribed in a ci...
Solutions for Chapter 5.1: Areas and Distances
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 5.1: Areas and Distances
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus,, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.1: Areas and Distances includes 26 full stepbystep solutions. Calculus, was written by and is associated to the ISBN: 9780534393397. Since 26 problems in chapter 5.1: Areas and Distances have been answered, more than 47399 students have viewed full stepbystep solutions from this chapter.

Average velocity
The change in position divided by the change in time.

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Cube root
nth root, where n = 3 (see Principal nth root),

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Independent variable
Variable representing the domain value of a function (usually x).

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Orthogonal vectors
Two vectors u and v with u x v = 0.

Square matrix
A matrix whose number of rows equals the number of columns.

Statistic
A number that measures a quantitative variable for a sample from a population.

Terminal side of an angle
See Angle.

Tree diagram
A visualization of the Multiplication Principle of Probability.

Unbounded interval
An interval that extends to ? or ? (or both).

Unit vector
Vector of length 1.