- 4.1: Using a Function Let (a) Find (b) Find and (c) Use a graphing utili...
- 4.2: Parabolic Arch Archimedes showed that the area of a parabolic arch ...
- 4.3: In Exercises 3 and 4,(a) write the area under the graph of the give...
- 4.4: In Exercises 3 and 4,(a) write the area under the graph of the give...
- 4.5: Fresnel Function The Fresnel function is defined by the integral (a...
- 4.6: Approximation The Two-Point Gaussian Quadrature Approximation for i...
- 4.7: Extrema and Points of Inflection The graph of the function consists...
- 4.8: Falling Objects Galileo Galilei (15641642) stated the following pro...
- 4.9: Use the techniques of this chapter to verify this proposition.
- 4.10: Use the techniques of this chapter to verify this proposition.
- 4.11: Riemann Sum Use an appropriate Riemann sum to evaluate the limit li...
- 4.12: Riemann Sum Use an appropriate Riemann sum to evaluate the limit
- 4.13: Proof Suppose that is integrable on and for all in the interval Pro...
- 4.14: Using a Continuous Function Let be continuous on the interval where...
- 4.15: Velocity and Acceleration A car travels in a straight line for 1 ho...
- 4.16: Proof Prove that if is a continuous function on a closed interval then
- 4.17: Verifying a Sum Verify that by showing the following. (a) (b) (c)
- 4.18: Sine Integral Function The sine integral function is often used in ...
- 4.19: Comparing Methods Let where is shown in the figure. Let and represe...
- 4.20: Minimizing an Integral Determine the limits of integration where su...
Solutions for Chapter 4: Calculus 10th Edition
Full solutions for Calculus | 10th Edition
Additive inverse of a real number
The opposite of b , or -b
See Inverse secant function.
An angle whose vertex is the center of a circle
Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row
See Ellipse, Hyperbola, Parabola.
The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.
Law of cosines
a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, c2 = a2 + b2 - 2ab cos C
Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.
Projection of u onto v
The vector projv u = au # vƒvƒb2v
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.
Real number line
A horizontal line that represents the set of real numbers.
Reciprocal of a real number
See Multiplicative inverse of a real number.
A statistical measure that does not change much in response to outliers.
Spiral of Archimedes
The graph of the polar curve.
A matrix whose number of rows equals the number of columns.
Symmetric difference quotient of ƒ at a
ƒ(x + h) - ƒ(x - h) 2h
A point that lies on both the graph and the y-axis.
Zero factor property
If ab = 0 , then either a = 0 or b = 0.