An Elementary Treatise on GraphsMacmillan & Company, 1904 - 183 páginas |
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Termos e frases comuns
abscissae angle approximately asymptotes average gradient average velocity axes axis calculate called centre circle common logarithm complete graph conic conic section constant coordinates satisfy corresponding values cosine crosses the x-axis cubic equation Cubic Function diagram distance Draw the graph ellipse equal example EXERCISES exponential function Find the average Find the equation fraction give Graph the equation Graph the function graphically Hence horizontal hyperbola inches increases left step length line given maximum method obtained origin parabola parallel perpendicular Plot the points point moves points of intersection positive values quadrant quotient radians radius real root represents scale SIMPLE HARMONIC MOTION simple sine curve simultaneous equations Solve the equation square straight line student t₁ tangent temperature trigonometric function turning point turning values values of x x-axis y-axis y-scale y=x³ zero
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Página 146 - PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant.
Página 147 - In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.
Página 48 - A can do a piece of work in 3 days, and B can do it in 5 days.
Página 149 - conic' is the locus of a point P which moves so that its distance from a fixed point S, called the 'focus,' is in a constant ratio to its distance from a fixed line called the 'directrix.
Página 135 - ... according as this limit does or does not exist. The geometry of curves is merely one of many departments of mathematics in which the idea of a derivative finds an application. Another important application is in dynamics. Suppose that a particle is moving in a straight line in such a way that at time t its distance from a fixed point on the line is <p(t). Then the 'velocity of the particle at time t' is by definition the limit of ) -#(0 h Examples XXXIX.
Página 101 - Art. 12O3. in which/ is the pressure in pounds per square inch, and V the volume in cubic feet of a pound of steam at the given pressure. •WORK DONE IN THE CYLINDER OF A STEAM ENGINE. Let P = the pressure on the piston in pounds per sq. ft. ; p = pressure on piston in pounds per sq. in. ; V = volume swept through by the- piston; W '=• work in foot-pounds.
Página 115 - An open tank is to be constructed with a square base and vertical sides so as to contain a given quantity of water. Show that the expense of lining it with lead will be least if the depth is made half of the width.
Página 156 - Prove that the area of the parallelogram formed by the tangents at the extremities of two conjugate diameters of an ellipse is constant, and is equal to 4 06.
Página 49 - Noon 1 PM 2 PM 3 PM 4 PM 5 PM 6 PM 7 PM 8 PM 9 PM 10 PM...