# Analytic Geometry and Calculus

Ginn, 1917 - Calculus - 516 pages

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### Contents

 Problems 55 The pointslope equation 57 The twopoint equation 58 Angles 59 Distance of a point from a straight line 63 Problems i 64 CERTAIN CURVES TW 34 Locus problems 69 3537 The circle y 70 4143 The hyperbola 77 4445 The parabola 80 The conic 83 47 The witch 84 The cissoid 85 The strophoid 86 Use of the equation of a curve 88 Empirical equations 89 Problems 92 80 97 89 98 PARAMETRIC REPRESENTATION 52 Definition 106 The circle 108 The cycloid 109 The trochoid 110 Article Page 57 The epicycloid 111 The hypocycloid 112 Problems 113 Coordinate system 118 The spirals 120 The straight line 121 The circle 122 The limacon 123 Relation between rectangular and polar coordinates 124 The conic the focus being the pole 125 Examples 126 Problems 127 Limits 130 Theorems on limits 132 Slope of a curve 134 Increment 135 Continuity 136 Differentiation of a polynomial 137 Sign of the derivative 138 Tangent line 140 The differential 141 Area under a curve 143 Differential of area 146 The definite integral 147 Problems 150 DIFFERENTIATION OF ALGEBRAIC FUNCTIONS 82 Theorems on derivatives 154 Derivative of 159 Higher derivatives 162 Article Page 164 DIFFERENTIATION OF TRANSCENDENTAL 192 Limit of 1 + 199 INTEGRATION 222 APPLICATIONS OF INTEGRATION Article Page 123124 Element of a definite integral 260 Area of a plane curve in Cartesian coordinates 262
 Center of pressure 277 Center of gravity 278 Attraction 283 Problems 285 SPACE GEOMETRY 139 Functions of more than one variable 300 Rectangular coordinates 301 Cylinders 303 Other surfaces 304 Surfaces of revolution 309 Projection 310 Components of a directed straight line 312 Distance between two points 313 Direction cosines 314 Angle between two straight lines 315 Direction of the normal to a plane 316 Equations of a straight line 817 317 direction 318 Determination of the direction cosines of a straight line 319 Distance of a point from a plane 320 Problems on the plane and the straight line 321 Article Page 159 Space curves 322 Direction of space curve and element of arc 324 Tangent line and normal plane 326 PARTIAL DIFFERENTIATION 162 Partial derivatives 335 Higher partial derivatives 338 Increment and differential of a function of two variables 339 Extension to three or more variables 342 Directional derivative of a function of two variables 343 Total derivative of z with respect to a 344 The tangent plane 345 Maxima and minima 348 Exact differentials 349 Line integrals 353 Differentiation of composite functions 357 Problems 361 MULTIPLE INTEGRALS 173 Double integral with constant limits 369 Double integral with variable limits 371 Computation of a double integral 373 Double integral in polar coordinates 374 Area bounded by a plane curve 376 Moment of inertia of a plane area 377 Center of gravity of plane areas 379 Area of any surface 381 Triple integrals 385 Change of coordinates 388 Volume 389 Moment of inertia of a solid 390 Center of gravity of a solid 392 Attraction 393 Problems 394 INFINITE SERIES 187 Convergence 405 The comparison test for convergence 406 The ratio test for convergence 407 Article Page 409 DIFFERENTIAL EQUATIONS 438 Answers 481 Index 514

### Popular passages

Page 252 - Q(x) to obtain a quotient (polynomial of the form g. ) plus a rational function (remainder divided by the divisor) in which the degree of the numerator is less than the degree of the denominator.
Page 69 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...
Page 101 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.
Page 463 - The general solution is the sum of the complementary function and the particular integral.
Page 396 - Find the moment of inertia of the area of a circle of radius a about an axis perpendicular to the plane of the circle at any point on its circumference.
Page 101 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 187 - A rectangular box with a square base and open at the top is to be made out of a given amount of material.
Page 383 - C". Ex. 1. Find the area of an octant of a sphere of \ radius a. If the center of the sphere is taken as the origin of coordinates (fig.
Page 315 - It is a very important fact that the sum of the squares of the direction cosines of any straight line is unity.
Page 101 - A point moves so that the square of its distance from the base of an isosceles triangle is equal to the product of its distances from the other two sides. Show that the locus is a circle. 50. Prove that the two circles z2 + y2 + 2 G,z + 2 Ftf + Cj = 0 and x2 + y...