Analytic geometry and calculusGinn and Company, 1917 - 516 pages |
Contents
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Common terms and phrases
angle approaches zero area bounded asymptote ax² axis C₂ cardioid center of gravity chord circle cone constant corresponding curve cylinder d²y definite integral derivative determined differential direction direction cosines directrix distance dx dx dx dy dy dx ellipse equal expressed Find the area Find the center Find the equation Find the points Find the value formulas function graph Hence hyperbola hypocycloid inertia integral length limit moment of inertia ordinate P₁ parabola parabolic segment parallel to OX parametric equations perpendicular plane XOY points of intersection polar coördinates positive Prove quadrant radius rectangle rectangular respectively right circular sin² slope Substituting surface tangent line Transform the equation triangle variable velocity vertex volume whence x₁ y₁ ди ду дх
Popular passages
Page 225 - 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 74 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.
Page 42 - 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 288 - Squaring and adding equations (2), we have cos2a + cos2/8 + cos27 = l; (3) that is, the sum of the squares of the direction cosines of any straight line is always equal to unity.
Page 74 - 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 383 - It is evident that the absolute value of the sum of n quantities is less than, or equal to, the sum of the absolute values of the quantities.
Page 366 - If the center of the sphere is taken as the origin of coordinates and the axis of the cone as the axis of z, it is evident from the symmetry of the solid that x = y = 0. To find z, we shall use polar coordinates, the equations of the sphere and the cone being respectively r = a and <l, = a.
Page 132 - Since y is a function of u and u is a function of x, it follows that y is ultimately a function of x.
Page 107 - The proof is left for the student. 4. The limit of the quotient of two variables is equal to the quotient of the limits of the variables, provided the limit of the divisor is not zero. Let X and Y be two variables such that Lim A
Page 336 - B = 38° 47' 13. c = 16.73, B = 84° 11', C = 48° 7' 14. a = 800.4, B = 55° 1', C = 66° 19' 15. b = 1784, A = 40° 13', B = 70° 9