## A First Course in Infinitesimal Calculus |

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### Common terms and phrases

abscissa Accordingly algebraic angle applications approaches zero approximate axis becomes calculus called centre Chap CHAPTER circle constant continuous coördinates corresponding critical values curve decreasing definite denote derivative determine difference differential distance draw dx dx equal equation error EXAMPLES expressed feet figure Find finite formula fraction function geometrical given gives Hence inches increasing increment infinite infinitesimal instance integral length less limit maximum mean measured method moving namely negative Note obtained ordinate parabola particular passes positive problems quantity radius rectangle references relation represented respect result revolving Show shown side slope solving speed square student substitution Suppose surface symbol taken tangent theorem units variable varies volume x-axis

### Popular passages

Page 50 - 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 393 - 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 320 - 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 56 - 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 280 - 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 227 - Differentiating the first of these equations with respect to x, the second with respect to y, and the third with respect to z...

Page 143 - 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 37 - 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 120 - ... 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 121 - 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°.