An elementary treatise on the differential and integral calculus, with numerous examples

 
9781130140088: An elementary treatise on the differential and integral calculus, with numerous examples
View all copies of this ISBN edition:
 
 

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 Excerpt: ...of the tangent. Since the normal is perpendicular to the tangent at the point of tangency, its equation is, from (2), Eem.--To apply (2) or (3) to any particular curve, we substitute for----, or-=--,, its value obtained from the equation of the curve and expressed in terms of the co-ordinates of the point of tongency. EXAMPLES. 1. Find the equations of the tangent and normal to the ellipse ay + bh = aW. We find dJL=-x.... l=_TM. dx a2y' dx' ah/ and this value in (2) gives, y-y =-aYx-ar; which by reduction becomes, tfyy' + Wxx'--aW, which is the equation of the tangent; and y-y =dfx-x) is the equation of the normal. 2. Find the equations of the tangent and normal to the parabola y2 = 2px. We find f=P-,.:% =?-„ dx y dx y and this value in (2) gives y-y =5 (-), or yy'--y'2 = px--px'. But y' = 2px'; 101. Length of Tangent, Normal, Subtangent, Subnormal, and Perpendicular on the Tangent from the Origin. Let PT represent the tangent at the point P, PN the normal; draw the ordinate PM; then Subtangent--y the perpendicular from origin on tqngent _ aW " (a4y" + 6V2)' 2. Find the subtangent and subnormal to the Cissoid 3 Here 3. Find the value of the subtangent of y2 = 3x2--12, at x = 4. Subtangent = 3. 4. Find the length of the tangent to f = 2x, at x = 8. Tangent = 4/l7. 5. Find the values of the normal and subnormal to the cycloid (Anal. Geom., Art. 156). dx V2ry--y.'. Subnormal = V%ry--y2 = MO. Normal = V2ry--PO. It can be easily seen that PO is normal to the cycloid at P; for the motion of each point on the generating circle at the instant is one of rotation about the point of contact O, i.e., each point for an instant is describing an infinitely small circular arc whose centre is at O; and hence PO is normal to the curve, i.e., the normal passes...

"synopsis" may belong to another edition of this title.

(No Available Copies)

Search Books:



Create a Want

If you know the book but cannot find it on AbeBooks, we can automatically search for it on your behalf as new inventory is added. If it is added to AbeBooks by one of our member booksellers, we will notify you!

Create a Want

Other Popular Editions of the Same Title

9781236951564: An elementary treatise on the differential and integral calculus; with numerous examples

Featured Edition

ISBN 10:  1236951565 ISBN 13:  9781236951564
Publisher: RareBooksClub.com, 2013
Softcover

9781154692587: An Elementary Treatise on the Differential and Integral Calculus; With Numerous Examples

Genera..., 2010
Softcover

9781144092649: An Elementary Treatise On the Differential and Integral Calculus, with Numerous Examples

Nabu P..., 2010
Softcover