- 4.1: Let (a) Find (b) Find and (c) Use a graphing utility to approximate...
- 4.2: Let (a) Use a graphing utility to complete the table.(b) Let Use a ...
- 4.3: In Exercises 3 and 4, (a) write the area under the graph of thegive...
- 4.4: In Exercises 3 and 4, (a) write the area under the graph of thegive...
- 4.5: The Fresnel function is defined by the integral(a) Graph the functi...
- 4.6: The Two-Point Gaussian Quadrature Approximation for is(a) Use this ...
- 4.7: Archimedes showed that the area of a parabolic arch is equal to the...
- 4.8: Galileo Galilei (15641642) stated the following proposition concern...
- 4.9: The graph of the function consists of the three line segments joini...
- 4.10: A car is traveling in a straight line for 1 hour. Its velocity in m...
- 4.11: Prove x0f tx t dt x0 t0f v dv dt.
- 4.12: Prove baf x fx dx 12 f b2 f a2.
- 4.13: Use an appropriate Riemann sum to evaluate the limit 1 2 3 . . . nn...
- 4.14: Use an appropriate Riemann sum to evaluate the limit 15 25 35 . . ....
- 4.15: Suppose that is integrable on and for all in the interval Prove tha...
- 4.16: Let be continuous on the interval where on (a) Show that (b) Use th...
- 4.17: Verify thatby showing the following. (a)(b)(c)
- 4.18: Prove that if is a continuous function on a closed interval then
- 4.19: Let where is shown in the figure. Let and represent the Riemann sum...
- 4.20: The sine integral functionis often used in engineering. The functio...
Solutions for Chapter 4: Calculus of a Single Variable 8th Edition
Full solutions for Calculus of a Single Variable | 8th Edition
Addition property of equality
If u = v and w = z , then u + w = v + z
A theorem that gives an expansion formula for (a + b)n
The probability of an event A given that an event B has already occurred
The graph of the parametric equations
Differentiable at x = a
a(b + c) = ab + ac and related properties
The minimum, first quartile, median, third quartile, and maximum of a data set.
Integrable over [a, b] Lba
ƒ1x2 dx exists.
Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.
For a basic trigonometric function f, an identity relating f(x) to f(-x).
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.
Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.
An equation in r and ?.
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.
Standard representation of a vector
A representative arrow with its initial point at the origin
Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.