A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 152
x = a, y has but one value, 6. Theseare the critical values of x and y. Upon the point(0, h), we observe that the branches do not passthrough it; since for x negative y is imaginarj^Hence (0, b) is not a multiple point. But uponthe point (a, b) we observe that y has two realvalues on each side of… … SINGULAR POINTS. 123 to the curve at the point make angles with the axis of x whose tangents are-f- \/o„ and — s/a. The form of the curve is given in the figure. Ex. 2. Examine y^ == x^ — x^ for multiple points. Ex. 3. Examine x^ -{- 2ax^y — ay^=0 for multiple points. Solution.—As it is not easy to…
Geometry, Analytic · Calculus
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