Elementary Functions and Applications

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Contents

Discussion of the Table of Values
21
Functions becoming Infinite Asymptotes
25
Variation of a Function
31
Average Rate of Change of a Function
34
Classification of Functions
38
Summary
40
CHAPTER II
46
Characteristic Property of a Straight Line
49
Slope of a Straight Line
51
Graphical Solution of Problems involving Functions which Change Uniformly
54
Graph of the Linear Function mx + b
56
Variation
61
Uniform Acceleration
63
Equation of a Straight Line
66
Application to the Solution of Problems
69
Remarks on Measurements
72
Possible Errors in Arithmetic Calculations Abridged Mul tiplication and Division
74
Empirical Data Problems
78
CHAPTER III
87
Graphs of ax2 and afx
88
Translation of the Co÷rdinate Axes
89
Instantaneous Velocity
93
Rate of Change Slope of Tangent Line
94
Graph of the Quadratic Function ax2 + bx + c
98
Empirical Data Problems
104
The Function x
107
Graph of x n 1
110
Graph of x 0 n 1 Graphs of Inverse Functions
113
Graph of x n 0 Graphs of Reciprocal Functions
117
Summary of Graph of x
119
Interpolation
121
Variation
125
Empirical Data Problems
127
The Linear Fractional Function
131
Integral Rational Functions
133
Synthetic Division
134
Graph of a Polynomial
136
Extent of the Tables
137
Solution of Equations Rational Roots
140
Translation of the yaxis
144
Horners Method of Solution of Equations
147
Graph of the Function f ax
150
Related Functions and their Graphs
151
Some Operations of Algebra regarded as Properties of Func tions
153
CHAPTER IV
158
Angles of any Magnitude
164
Trigonometric Functions of any Angle
165
Radians
170
Graphs of the Trigonometric Functions
172
Functions of Complementary Angles
177
Tables of Trigonometric Functions
178
Solution of Right Triangles
180
Applications
183
Parallelogram Law Velocities Accelerations Forces
185
Conditions of Equilibrium of a Particle
187
Functions of n90║ 0
192
Application to the Use of Tables
196
Inclination and Slope of a Straight Line
199
Law of Sines
201
Law of Cosines
202
Solution of Oblique Triangles
203
Computation by Means of Common Logarithms
229
Solution of Triangles
233
Exponential Equations
237
Compound Interest
241
Annuities
244
Graph of the exponential function kbnz
248
The Logarithmic Scale
249
Empirical Data Problems
256
CHAPTER VI
264
Limits
265
Derivative of a Function
267
Fundamental Formulas for Differentiation
269
Derivative of a Polynomial
271
Corresponding Properties of a Function its Graph and its Derivative
272
Velocity and Acceleration
276
Derivative of a Rational Function
278
Derivative of an Irrational Function
279
Equations of Tangent and Normal Lines
281
Problems in Maxima and Minima
285
Related Rates
289
Small Errors
291
Approximate value of f x + Ax
296
CHAPTER VII
301
Area under a Curve
304
Motion in a Straight Line
308
Motion in a Plane
311
Volume of a Right Prism
315
Volume of a Right Circular Cylinder
318
Volume of a Pyramid
320
Volume of a Solid of Revolution
323
Volume of a Cone of Revolution
325
Volume of a Sphere
328
CHAPTER VIII
332
Trigonometric Equations
334
Trigonometric Identities
336
Functions of the Sum of Two Angles
338
Functions of the Difference of Two Angles
341
Functions of Twice an Angle or the Functions of Any Angle in Terms of Half the Angle
342
Functions of Half an Angle or Functions of Any Angle in Terms of Functions of Twice the Angle
343
Sum and Difference of the Sines or Cosines of Two Angles
345
Logarithmic Solution of Triangles Case III
346
Logarithmic Solution of Triangles Casc IV
348
Miscellaneous Identities and Equations
351
Differentiation of Trigonometric Functions
352
Graph of the Function a sin bx + c Harmonic Curves
358
Empirical Data Problems
361
CHAPTER IX
365
Permutations
366
Combinations
367
The Binomial Expansion
370
Probability
373
Compound Events
375
Mortality Tables
379
Frequency Distributions
382
Averages
388
Measures of Variability
398
Equation of the Frequency Curve Representing a Sym
404
The Probable Error
411
Correlation
420
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Page 368 - This is the same as the number of permutations of n things taken r at a time, and hence r!C(╗,r) = P(ź,r) '-- It is interesting to know that the number of combinations of n things taken r at a time is the same as the number of combinations of n things taken n — r at a time.
Page 223 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page xviii - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page xviii - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 171 - A radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
Page 223 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 289 - Now all know that the intensity of illumination varies inversely as the square of the distance.
Page 155 - It is found that the quantity of work done by a man in an hour varies directly as his pay per hour and inversely as the square root of the number of hours he works per day. He can finish a piece of work in six days when working 9 hours a day at Is.
Page 181 - You have learned that the tangent of an acute angle of a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle.
Page 368 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.

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