A First Course in Infinitesimal Calculus |
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Common terms and phrases
abscissa Accordingly algebra angle anti-differential approaches zero arbitrary constants asymptotes axis cardioid centre Chap CHAPTER chord circle continuous function convergent convergent series cos² critical values cubical parabola curvature cylinder d²y d³y definite integral denote derivative Diff differential equation distance dx dx dx dy dy dx ellipse EXAMPLES expression Find the area Find the volume finite formula fraction function geometrical given Hence hyperbola hypocycloid hysin infinite series infinitesimal integral curve intersection interval length limit NOTE obtained ordinates parabola y² plane polar coördinates radius rectangle respect result revolution revolving Rolle's theorem sec² second member sector Show sin² sin³ slope square substitution subtangent surface tangent Taylor's theorem theorem trigonometry Va² variable x-axis y-axis ду дх
Popular passages
Page 326 - From eight times the chord of half the arc, subtract the chord of the whole arc, and divide the remainder by 3, and the quotient will be the length of the arc, nearly.
Page 286 - A straight line moves so that the sum of the squares of the perpendiculars on it from two fixed points (± c, 0) is constant (=2 k-) : show that its envelope is the conic -- k- E- = 1.
Page 233 - Differentiating the first of these equations with respect to x, the second with respect to y, and the third with respect to z...
Page 39 - x". It is not "dy" divided by "dx" or "d" multiplied by "y" divided by "d" multiplied by "x." In precise mathematical terms a derivative of a function is the limit of the ratio of the increment of the function to the increment of the independent variable when the latter increment varies and approaches zero as a limit.
Page 126 - ... the following problems the cones and cylinders are supposed to be right cones and cylinders on circular bases.] 48. Determine the greatest cylinder that can be inscribed in a given cone.
Page 398 - ... the minor axis when they are drawn at equal angular intervals, and is equal to half the major axis when they are drawn so that the abscissas of their extremities increase uniformly. (6) Suppose a straight line divided at random into three parts ; find the mean value of their product. | o3 '"
Page 58 - 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 399 - A rectangular sheet of metal has four equal square portions removed at the corners, and the sides are then turned up so as to form an open rectangular box.
Page 242 - A, the semi-major axis a, and the semi-minor axis 6. 5. A rectangle moves from a fixed point, one side varying as the distance from the point, and the other side as the square of this distance.
Page 203 - Find the volume of a sphere of radius a, considering the sphere as generated by the revolution of a circle about one of its diameters.