An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

CHAP. XI.

MISCELLANEOUS EXAMPLES.
1. IT is required to trace or describe the common parabola whose equation is y2= 4ax. See the second Diagram of
page (304) with the axes of x and y interchanged.
2. Trace the parabolic curve whose equation is a y3 = v4.
See the second Diagram of page (304).
3. Determine the form of the curve defined by the equation ay2 = 3. See the Diagram of page (338).
4. Required the form of the curve whose equation is
a2y = 3. See the Diagram of page (303).
5. Trace the curve defined by the equation y3 = a2.
See the Diagram of page (303) reversed.
6. Trace the curve whose equation is (y- a)2=4a ( - a).
See the second Diagram of page (304) with a new origin and
the axes interchanged.
7. Find the form of the figure belonging to the equation
a (y + b)3 = (x - a)4. See the Diagram just referred to.
8. The equation of a curve being a (y -b)2= ( - c)3,
find its figure. See the Diagram of page (338) with a new
origin and parallel axes.
9. What is the form of the curve defined by the equation
a2 (y - b) = (x + a)3? See the Diagram of page (303) with
a new origin and parallel axes.
10. Trace the curve whose equation is x4 - bx3 = a3y. See
the Diagram of page (346) inverted.