A Treatise on the Differential Calculus and the Elements of the Integral Calculus: With Numerous ExamplesMacmillan, 1864 - 404 σελίδες |
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Σελίδα 3
... proceed to another example more important for our purpose . Suppose y = 1 + ' and consider the series of values which y assumes when to 3C are assigned different positive values . When x = 0 , y = 0 , and when x has any positive value ...
... proceed to another example more important for our purpose . Suppose y = 1 + ' and consider the series of values which y assumes when to 3C are assigned different positive values . When x = 0 , y = 0 , and when x has any positive value ...
Σελίδα 5
... proceed further with the ex- ample ; the reader will see that when z is greater than unity y is positive ; that y continually diminishes as z increases , and approaches the limit unity when z increases indefinitely . 12. The student has ...
... proceed further with the ex- ample ; the reader will see that when z is greater than unity y is positive ; that y continually diminishes as z increases , and approaches the limit unity when z increases indefinitely . 12. The student has ...
Σελίδα 7
... proceed to demonstrate , is very important . increases indefinitely the expression ( 1+ certain limit which lies between 2 and 3. " In the first place suppose x a positive whole number , = m say ; we shall prove that the above ...
... proceed to demonstrate , is very important . increases indefinitely the expression ( 1+ certain limit which lies between 2 and 3. " In the first place suppose x a positive whole number , = m say ; we shall prove that the above ...
Σελίδα 18
... proceeds in the subject and finds that in many cases possesses the properties of an algebraical fraction . We remark ... proceed to draw and express by means of our definitions and symbols . The following notation is also frequently used ...
... proceeds in the subject and finds that in many cases possesses the properties of an algebraical fraction . We remark ... proceed to draw and express by means of our definitions and symbols . The following notation is also frequently used ...
Σελίδα 22
... proceed to the rules for determining the differential coefficient of any known algebraical expression , we shall give some geometrical illustrations which will assist in forming a conception of the meaning of a differential coefficient ...
... proceed to the rules for determining the differential coefficient of any known algebraical expression , we shall give some geometrical illustrations which will assist in forming a conception of the meaning of a differential coefficient ...
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A Treatise On the Differential Calculus and the Elements of the Integral ... Isaac Todhunter Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
Συχνά εμφανιζόμενοι όροι και φράσεις
angle asymptote axis binomial theorem centre chord circle of curvature constant cycloid d'u d'u d²u d³u d³y deduce denote determine dF dF Differential Calculus differential coefficient diminish without limit du du dx dx dy dx dy dx dx dz dx² dx³ dy dy dy dz dy² dz dx dz dy dz dz eliminate ellipse example expression finite fraction given curve given equation Hence hn+1 increases indefinitely independent variable locus maxima and minima maximum or minimum minimum value negative numerator obtain parabola perpendicular point of inflexion positive preceding article proper fraction quantities respect Result shew St John's College subtangent Suppose tangent Taylor's Theorem tion triangle ultimate intersections unity vanish x₁ zero Δη аф
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Σελίδα 231 - Determine a point within a triangle, such that the sum of the squares of the distances from the three sides is a minimum.
Σελίδα 336 - Shew that in general a conic section may be found which has a contact of the fourth order with a given curve at a proposed point, and shew how to find it when the length of the curve is given in terms of the angle which the normal makes with a fixed line. If the curve be an equiangular spiral, and a be the angle between the radius vector and the tangent at any point, shew that the conic section is an ellipse, the major axis of which makes with the normal to the curve an angle o> given by the equation...
Σελίδα 361 - A given curve rolls on a straight line, explain the method of finding the locus of the centre of curvature at the point of contact of the curve and straight line. If the rolling curve be an equiangular spiral the required locus will be a straight line ; if a cycloid a circle ; and if a catenary a parabola.
Σελίδα 268 - In the curve x*y* = a* (x + y], the tangent at the origin is inclined at an angle of 135° to the axis of a:. 4. In the curve x" (x + y) = a' (x—y), the equation to the tangent at the origin is y = x.
Σελίδα 197 - A person being in a boat 3 miles from the nearest point of the beach, wishes to reach in the shortest time a place 5 miles from that point along the shore ; supposing he can walk 5 miles an hour, but row only at the rate of 4 miles an hour, required the place he must land.
Σελίδα 323 - The chord of curvature passing through the origin will be obtained by multiplying 2p by the cosine of the angle between the radius vector and the normal to the curve at the point considered. (Art. 320.) Hence the chord of curvature through the origin 324. If i/r be the angle which the tangent at the point (x, y) of a curve makes with the axis of x, we have , dx therefore -=*- = dy dfy dx3 dx dx* ds (dy\* ds + (dx) Г"Чй.
Σελίδα 200 - Of all the lines drawn from the vertex of a given ellipse to the circumference of the circumscribing circle, determine that for which the portion intercepted between the two curves is a maximum. If...