This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 edition. Excerpt: ...d2?' 3 a.. dz 2 dx2 4/x It is readily seen that the curve is symmetrical with respect to the X-axis and lies wholly to the right of the Y-axis. At the origin the slope is zero, and the two branches of the curve have the X-axis as a common tangent; the origin is therefore a cusp. There is no point of ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 edition. Excerpt: ...d2?' 3 a.. dz 2 dx2 4/x It is readily seen that the curve is symmetrical with respect to the X-axis and lies wholly to the right of the Y-axis. At the origin the slope is zero, and the two branches of the curve have the X-axis as a common tangent; the origin is therefore a cusp. There is no point of inflexion. Hence the curve has the general form shown in Fig. 37. Y Y Y. O X 0 X 0 X z = 2a, which is an asymptote. For x = 0, 3i: 0, showing that the X-axis is a tangent to both branches at the origin. An investigation of the second derivative shows that there is no point of infiexion and that both branches are.convex towards the X-axis. The curve has therefore the general form shown in Fig. 38. _slin. x' ] 4 a2 to the Y-axis. y has a maximum value 2 a for x = 0, and there are points FIG. 39. FIG. 40. Ex. 3. The witch y = The curve is symmetrical with respect Ex. 4. The lemnz'scate p2: a2 cos 2 0, or (e +: we--r)The curve is symmetrical with respect to both axes, and crosses the X-axis at x = i a. For values of 0 from 71,1r to %1r and from g 1r to in, p is imagi nary. The origin is a double point, the tangents having the slopes--1 and 1, respectively. The curve has the form shown in Fig. 40. cord of uniform weight suspended trom two fixed points. The curve is symmetrical about the Y-axis, and cuts the Y-axis at a distance a above the origin. The second derivative is positive for all values of x, hence the curve is concave upwards and has no point of inflexion. See Fig. 41. FIG. 41. FIG. 42. Ex. 6. The cycloid is the curve described by a-point on the circumference of a circle which rolls on a straight line. Let (1 denote the radius of the circle, and 0 the angle POM Fig. 42, subtended by the arc PM(: OM). Then we have for the...
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Add this copy of Essentials of Calculus to cart. $56.22, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2010 by Nabu Press.
Add this copy of Essentials of Calculus to cart. $56.46, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2010 by Nabu Press.
