 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 TwoPoint 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
ISBN: 9781285057095
Solutions for Chapter 4
Get Full SolutionsSince 20 problems in chapter 4 have been answered, more than 2705 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4 includes 20 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus, edition: 10. Calculus was written by and is associated to the ISBN: 9781285057095.

Additive inverse of a real number
The opposite of b , or b

Arcsecant function
See Inverse secant function.

Central angle
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

Focus, foci
See Ellipse, Hyperbola, Parabola.

Heron’s formula
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

Probability function
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

Quadratic function
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.

Quartile
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.

Resistant measure
A statistical measure that does not change much in response to outliers.

Spiral of Archimedes
The graph of the polar curve.

Square matrix
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

yintercept
A point that lies on both the graph and the yaxis.

Zero factor property
If ab = 0 , then either a = 0 or b = 0.