A First Course in Infinitesimal Calculus |
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Common terms and phrases
abscissa Accordingly algebraic angle anti-differential arbitrary constant area APQB asymptotes centre Chap chapter chord circle continuous function convergent convergent series cos² critical values cubical parabola curvature cylinder definite integral denote Diff distance dx dx dx dy dy dx ellipse equal EXAMPLES expressed Find the area Find the volume finite formula fraction function geometrical given Hence hyperbola increment infinite number infinite series infinitesimal Integral Calculus integral curve interval length limit method notation NOTE number of units obtained ordinates parabola y² plane points of inflexion polar coördinates positive radius rectangle respect result revolving Rolle's theorem sec² second member Show sin² slope substitution subtangent surface tangent Taylor's theorem theorem trigonometry Va² variable x-axis x-derivative y-axis ду дх მყ
Popular passages
Page 52 - PROP. II. Product of Constant and Function. The differential coefficient of a product of a constant and a function of x is equal to the product of the constant and the differential coefficient of the function, or, stated...
Page 395 - The lower corner of a leaf, whose width is a, is folded over so as just to reach the inner edge of the page. Find the width of the part folded over, when the length of the crease is a minimum.
Page 322 - 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 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 282 - A straight line moves so that the sum of the squares of the perpendiculars on it from two fixed points (± c, 0) is constant (= 2fc'2) : show that y2 y'2 its envelope is the conic — - ( + ^ = 1.
Page 229 - Differentiating the first of these equations with respect to x, the second with respect to y, and the third with respect to z...
Page 145 - Nova methodus pro maximis et minimis, itemque tangentibus, quae nee fractas nee irrationales quantitates moratur, et singulare pro illis calculi genus, die in den Actis Erudit.
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 122 - ... 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 123 - From a given circular sheet of metal it is required to cut out a sector so that the remainder can be formed into a conical vessel of maximum capacity ; prove that the angle of the sector removed must be about 66°.