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

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126. Required the magnitudes and positions of the greatest and least radii vectores in the curve defined by the polar
a
equation r = - e co
1 + e cos 0
127. Find the positions and magnitudes of the greatest
and least radii vectores in the curve whose equation is
r2 - a2 sin 2 0.
128. Determine the maximum or minimqnum radius vector
in the curve whose polar equation is r cos 0= a (1.-cos 0).
129. Find the magnitude and position of the maximumi
or minimum radius vector of the Lituus, whose equation is
r"0 = C2.
130. Determine whether the spiral whose equation is
r (e0 + e-) 2a,
admits of a maximrnm or minizmum radius vector, and decide
which it is.
131. Find the singular points of the spiral whose equation is r=a sin 20.
132. Determine the singular points of the polar curves
whose equations are r'- a2 cos2 0 + b2 sin' 0.
133. Find the positions and natures of the singular
points in the curve whose polar equation is r a ( + cos 0).
134. In the polar curve defined by the equation
2r (sin3 0 - cos3 0) = a sin 20,
it is required to find the positions and natures of the sin-,
gular points.