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

9 9

100. The equation of a cur ve being.
jtis, required -to shew that there is a cusp of the first species
corresponding to v 1 and y =0: a nd to find its tangoent.
101. The - equation of 'a curive be~ing -'ay (x - a),
it is required to prove the existence of two cusps of the first
species corresponding to v a and y =_ 0: and to find the
directions of their tangents.
10,2. The curve defined by the equation
a2y2 2 a%,2y = 3x'~bx3,
has two cus ps ''of the~_ flirst species corresponding to x0
Y 0, ad x b y= required a proof: and find.
the" positions of:their tangents..103. The equation of a curve being 4 ay= (X - 2
it is required to prove the existence of two, cusps of the-flrst
speces crresondig to v =+~a and y=0: and, to fi nd thedirections of their tangents.
104. Linthe curve defined by the equation,
5
'y-a=bi,2 ~"e- i)2,
it. is required to -prove -the existence of a cusp of -the second
'specie s correspon'ding, to x =1 and y =,a +b: and to find the
position of its' rectilineal tangent.
105. If the equation of a curve be
(2a+ _ - X2 =X Ga )2
~it 'is required to priove the existence of a cusp of the second
species whrien x =I1 and y =- -I1: and to find the direction
of its- taget-irt