- 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 12-second 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
The change in position divided by the change in time.
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.
The real number multiplied by the variable(s) in a polynomial term
nth root, where n = 3 (see Principal nth root),
The factor Ae-a in an equation such as y = Ae-at 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.
Variable representing the domain value of a function (usually x).
Left-hand 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
The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space
Two vectors u and v with u x v = 0.
A matrix whose number of rows equals the number of columns.
A number that measures a quantitative variable for a sample from a population.
Terminal side of an angle
A visualization of the Multiplication Principle of Probability.
An interval that extends to -? or ? (or both).
Vector of length 1.