## Analytic Geometry and Calculus |

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### Common terms and phrases

angle approaches zero area bounded assume asymptote axis axis of x base called cardioid center of gravity chord circle coefficients cone constant converges corresponding values cosx curve cylinder definite integral denote derivative determined direction direction cosines directrix distance dx dx ellipse equal expressed Find the area Find the center Find the equation Find the points Find the value formula fraction function given graph Hence hyperbola hypocycloid increases increment inertia integral limit line is drawn moment of inertia negative ordinate origin parabola parallel to OX parametric equations perpendicular plane XOY points of inflection points of intersection polar coordinates positive problem quadrant rectangle represented respectively result right circular slope solution sphere straight line joining Substituting surface tangent line triangle variable velocity vertex vertices volume whence

### 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...