By Shafarevich I.R.

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For example, y 2 - X = 0 has two ranges in y, one positive and one negative, while the 23 explicit form derived from solving the above equation gives y = Xl/2, for which the range of y is positive only; in such cases both the positive and the negative range of yare plotted. REFERENCES 1. Buck, R. , Advanced Calculus, McGraw-Hill, New York, 1965, Chap. 5. 2. , and I. Stewart, Catastrophe Theory and Its Applications, Pitman, New York, 1978. 3. , and I. A. , 1964. 4. Mandelbrot, B. , The Fractal Geometry of Nature, W.

3. 4. 1. 2. 3. 5. Y = c/[x(a 2 + x 2 )] 1. 02 2. 02 3. 6. 1. 2. 3. 7. 1. 2. 3. 02 2. 3. 8. y 1. 4. 1. Y = c/(a 2 1. 2, c = 2. 5, c = 3. 2. Y = cx/(a 2 - x 2 ) 1. 1 2. 1 3. 3. 1. 2. 3. 4. Y = cx 3 /(a 2 - x 2 ) 1. 2 2. 2 3. 5. Y = c/[x(a 2 - x 2 )] 1. 001 2. 001 3. 6. Y = 1. a = 2. a = 3. 7. 1. 2. 3. 8. Y = cx 2 (a 2 1. 2, c = 2. 5, c = 3.

2. 1. 2. 3. 3. y = c(a + bX)3 y - b 3cX 3 - 3ab 2cx 2 - 3a 2bcx -a 3 c 1. 2. 3. 4. 1. 2. 3. 5. y = cx(a + bX)2 1. 0 2. 0 3. 6. y 1. 2. 3. 7. Y 1. 2. 3. 8. Y = cx 2(a 1. 2. 3. 9. Y = cx 2(a y - b 3cX 5 + bx? -a 3 cx 2 1. 2. 3. 10. Y = cx 3(a + bx) 1. 0 2. 0 3. 11. Y = cx 3(a + bX)2 1. 0 2. 0 3. 12. y = cx3(a 1. 2. 3. 13. y = e/(a + bx) 1. 02 2. 02 3. 14. y = e/(a + bX)2 1. 02 2. 02 3. 15. y = e/(a + bX)3 a 3y + 2a 2bxy + 2ab 2 x 2 y + b 3x 3y =0 1. 2. 3. 16. y = ex/(a + bx) 1. 1 2. 1 3. 17. y = ex/(a + bX)2 1.