Analytic Geometry: With Introductory Chapter on the Calculus |
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Other editions - View all
Analytic Geometry: With Introductory Chapter on the Calculus Claude Irwin Palmer,William Charles Krathwohl No preview available - 2015 |
Analytic Geometry: With Introductory Chapter On the Calculus Claude Irwin Palmer,William Charles Krathwohl No preview available - 2022 |
Common terms and phrases
abscissa algebraic analytic geometry angle Ax² axis parallel bisects chords circle conic conjugate hyperbolas constant coördinate axes coördinate planes cos² determined diameter direction cosines directrix distance dx dx dx dy dx dy dx dy ellipse equa equal Example 2.-Find EXERCISES Find the coördinates Find the equation foci focus formulas function given gives Hence hyperbola intercepts l₁ latus rectum line 2x line joining line parallel line passes line segment locus m₁ major axis nates negative ordinate origin P₁ P₁P2 P₂ parabola y² parametric equations perpendicular points of intersection polar coördinates positive quadrant r₂ radians radius rectangular coördinates semimajor axis shown in Fig sin² slope Solving straight line Substituting surface symmetrical with respect tangent transverse axis triangle values variable vertex vertices x-axis xy-plane y-axis y-intercept y₁ yz-plane z-axis
Popular passages
Page 228 - The derivative of the product of two functions is equal to the first function times the derivative of the second plus the second times the derivative of the first. (4) 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 1 - As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection.
Page 95 - Find the locus of a point, the distances of which from two given straight lines have a fixed ratio. 143. Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 220 - This illustration will serve to introduce the definition of the next section. 476. Limit of a Variable. When the successive values of a variable approach a certain constant number so that the difference between the constant and the variable becomes and remains less than any assigned positive number, however small, then the constant is called the limit of the variable. 477. The statement "x approaches the limit a," where x is a variable and a is a constant, is sometimes written x = a, the symbol =...
Page 228 - The derivative of the product of a constant and a function is equal to the constant times the derivative of the function; that is, if y = cu, ihen dy _ d(cu) du dx dx dx 3.
Page 95 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 134 - The parabola is the locus of a point whose distance from a fixed point, the focus, is always equal to its distance from a fixed line, the directrix.
Page 117 - By definition [§ 69], the ellipse is the locus of a point whose distance from a fixed point, the focus, divided by its distance from a fixed line, the directrix, is a constant e, less than 1. Let F be the focus ,' and SR the directrix. Through F take А' я с A tsFD perpendicular to SR at D. There is a point A between F and D such that FA/AD = e.
Page 83 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.
Page 221 - ... The limit of the sum, or product, of a constant and a variable is the sum, or product, of the constant and the limit of the variable. 3. The limit of the variable sum, or product, of two or more variables is the sum, or product, of their limits. 4. The limit of the variable quotient of two variables is the quotient of their limits, except when the limit of the divisor is zero. 54. Notation. The sign = denotes