Elements of the Differential and Integral Calculus: With Examples and Practical Applications |
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Elements of the Differential and Integral Calculus: With Examples and ... James William Nicholson No preview available - 2017 |
Elements of the Differential and Integral Calculus: With Examples and ... James William Nicholson No preview available - 2016 |
Common terms and phrases
angle asymptote axis b²x² BCDP BCP'P circle co-ordinates constant convergent cos² cos³ cosec d²u d³u d³y decreasing denoted derivative dx dx dx dy dx dx² dx³ dy dy dy² dy³ equal equation EXAMPLES Find the area Find the length Find the slopes Find the values finite fraction function h approaches hence increased by h increment independent variable INDETERMINATE FORMS intersection limit logarithms m₁ maxima maxima and minima maximum minimum value multiple points negative OBPA plane curve points of inflection quantity radius of curvature rate of change respect revolution roots sec² sin x sin² sin³ Solids of Revolution Substituting subtangent surface tan-¹ tangent varies disproportionally velocity x₁ x² dx y-turns y₁ Δυ
Popular passages
Page 218 - Geom., Prop. XXII., B. IV. Hence BG= VBCxBE= V2r(2r-y), and consequently the arc BD=2BG, or the arc of a cycloid, estimated from the vertex of the axis, is equal to twice the corresponding chord of the generating circle ; hence the entire arc BDA is equal to twice the diameter BC, and the entire curve ADBH is equal to four times the diameter of the generating circle.
Page 117 - ... isosceles triangle that can be described about a given ellipse, having its base parallel to the major axis. The height is three times the minor semi-axis. 15. Inscribe the greatest parabolic segment in a given isosceles triangle. The altitude of the segment is three-fourths that of the triangle. 16. A steamer whose speed is 8 knots per hour and course due north sights another steamer directly ahead, whose speed is 10 knots, and whose course is due west. What must be the course of the first steamer...
Page 48 - If a circular plate of metal expand by heat so that its diameter increases uniformly at the rate of...
Page 133 - A circle tangent to a curve at any point, having its concavity turned in the same direction, and having the same curvature as that of the curve at that point, is called the circle of curvature ; its radius, the radius of curvature ; and its centre, the centre of curvature.
Page 117 - ... shore ; he can pull at the rate of 4 miles an hour, but can walk at the rate of 5 miles an hour ; find the point at which he must land. Express the whole time in terms of the distance of the required point from the nearest point of the shore.
Page 73 - It may be extended to any number of differentiations; so that if a function of two independent variables, x and y, is to be differentiated m times with respect to x, and n times with respect to y, the result will be the same in whatever order the differentiations be performed. In proof of this we have only to apply the theorem of Art.
Page 229 - ... 5. Find the volume of the solid generated by the revolution of the closed part of the curve a?
Page 23 - ... changed into the differential of the denominator, divided by the square of the denominator. Let...
Page 137 - P=p, dJR_dr dP~d~p' therefore с = r -=- : dp that is, tlie radius of curvature = /•-,- . dp 328. At a point where the radius of curvature is a maximum or a minimum the circle of curvature has contact of the third order with the curve.
Page 228 - XII , 5) about its asymptote. 9. Find the surface generated by the revolution about the axis of x of the portion of the curve which is on the left of the axis of y.