Analytic Geometry and Calculus |
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Common terms and phrases
angle approaches zero area bounded asymptote ax² axes axis of x Cartesian equation center of gravity chord constant corresponding cos² curve cylinder derivative differential directrix distance dx dx dx dy dx² dy dx ellipse equal Find the area Find the center Find the equation Find the locus Find the parametric Find the value fixed circle foci formulas function graph Hence hyperbola hypocycloid increases increment initial line integral length limit line is drawn locus moment of inertia negative ordinate origin P₁ parabola y² parallel to OX parametric equations particle perpendicular points of intersection polar coördinates positive Prove quadrant radius respectively sin² slope strophoid surface tangent Transform the equation triangle variable velocity vertex volume whence x₁ y₁ дх
Popular passages
Page 246 - 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 63 - 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 95 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.
Page 457 - The general solution is the sum of the complementary function and the particular integral.
Page 390 - 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 95 - 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 181 - A rectangular box with a square base and open at the top is to be made out of a given amount of material.
Page 377 - 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 309 - It is a very important fact that the sum of the squares of the direction cosines of any straight line is unity.
Page 95 - 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...