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Contenido

 Graph of the Linear Function mx 20 Discussion of the Table of Values 21 Uniform Acceleration 22 Equation of a Straight Line 23 Application to the Solution of Problems 24 Functions becoming Infinite Asymptotes 25 Possible Errors in Arithmetic Calculations Abridged Mul tiplication and Division 26 Empirical Data Problems 27 Variation of a Function 28 72 29 Graphs of ax2 and afx 31 Instantaneous Velocity 32 Rate of Change Slope of Tangent Line 33 Average Rate of Change of a Function 34 Graph of the Quadratic Function ax˛ + bx + c 35 The Function 36 Classification of Functions 38 Summary 40 21 44 25 45 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 Common Logarithms 82 Graph of the exponential function kbno 88 Empirical Data Problems 104 Tables of Squares Cubes Square Roots Cube Roots and Reciprocals 107 Graph of x n 1 110 Graph of x 0 n 1 Graphs of Inverse Functions 113 Graph of n 0 Graphs of Reciprocal Functions 41 Summary of Graph of 119 Interpolation 121 147 122 Variation 125 Empirical Data Problems ax + 127 The Linear Fractional Function cx + d 131 Integral Rational Functions 47 The Remainder Theorem 133 Synthetic Division 49 Graph of a Polynomial 50 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 150 151 153 CHAPTER IV 158 Angles of any Magnitude 164 Trigonometric Functions of any Angle 165 Radians 170 Graphs of the Trigonometric Functions 171 Functions of Complementary Angles 177 Tables of Trigonometric Functions 178 Solution of Right Triangles 180 Applications 183 Parallelogram Law Velocities Accelerations Forces 185 107 187
 119 204 121 206 Inverse Trigonometric Functions 209 125 211 127 216 C 220 131 228 Area of a Sphere 231 133 233 136 235 137 236 140 248 144 250 CHAPTER VI 264 158 267 Derivative of a Polynomial 271 Derivative of a Rational Function 278 164 284 165 285 Small Errors 291 170 293 172 296 CHAPTER VII 301 Area under a Curve 308 177 309 180 312 Volume of a Right Prism 315 183 316 185 317 187 321 Volume of a Solid of Revolution 323 192 327 CHAPTER VIII 332 Functions of the Sum of Two Angles 338 196 339 Sum and Difference of the Sines or Cosines of Two Angles 345 199 350 Miscellaneous Identities and Equations 351 0 353 203 355 Graph of the Function a sin bx + c Harmonic Curves 358 CHAPTER IX 365 Probability 373 Mortality Tables 379 209 382 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 214 216 C 385 Averages 388 217 394 Measures of Variability + 398 219 401 Equation of the Frequency Curve Representing a Sym 404 Introduction 76 Graph of the Exponential Function bw b 1 410 The Probable Error 411 Correlation 420 Graph of the Logarithmic Function 81 Properties of the Logarithmic Function logo a b 1 434

Pasajes populares

Página 368 - This is the same as the number of permutations of n things taken r at a time, and hence r!C(»,r) = P(«,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.
Página 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.
Página xviii - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Página 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.
Página 289 - Now all know that the intensity of illumination varies inversely as the square of the distance.
Página 204 - Given two sides and an angle opposite one of them. The angle opposite the other given side is found by Theorem I. The third angle is obtained by subtracting the sum of the other two from 180°.
Página 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.
Página 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.
Página 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.
Página 320 - The vertices of the triangles form the vertex of the pyramid. The altitude of the pyramid is the perpendicular distance from the vertex to the base.