Analytic Geometry and Calculus |
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Common terms and phrases
angle approaches zero area bounded ax² axis cardioid center of gravity chord cone constant corresponding curve cylinder denoted derivative determined differential direction directrix distance dx dx dx dy dx² dy dx ellipse equal Find the area Find the center Find the equation Find the value foci formulas function graph Hence hyperbola hypocycloid increases increment initial line integral length limit line is drawn moment of inertia ordinate origin P₁ parabola parabola y² parallel to OX parametric equations particle perpendicular plane XOY points of inflection polar coördinates positive Prove quadrant radius rectangle respectively right circular sin² slope strophoid Substituting surface tangent line triangle variable velocity vertex volume whence x₁ y₁ ди ду дх
Popular passages
Page 251 - 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 100 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.
Page 409 - 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 68 - 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 314 - Squaring and adding equations (2), we have cos2« + cos2/9 + cos27 = 1 ; (3) that is, the sum of the squares of the direction cosines of any straight line is always equal to unity.
Page 100 - 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 293 - ... one inch in diameter, ground to a smooth surface, but left in a slightly greasy condition by their experience of being dropped into beds of tallow in their use six years ago. The mere buoyant effect of air on bronze may properly be neglected in this discussion, as it is very small. If we assume that the resistance of the air is proportional to the square of the velocity of the falling sphere, within the moderate range of velocity here considered, we have, as the net accelerating force on a ball...
Page 157 - The derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
Page 158 - 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 188 - A length I of wire is to be cut into two portions, which are to be bent into the forms of a circle and a square respectively. Show that the sum of the areas of these figures will be least when the wire is cut in the ratio TT : 4.