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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39. If x= b - m then willp + qy + =o.
40. 'Ifz=jS -(Y ), then will 2p y +q(4y2)=0
41. If 2 _ 22 == 2 z (c4 —) 9 then cap - qx- + vy= o.
42. If a?2 + y2 + 2 = (ax + by + t), then will
(y - b)p - ( - ) q=b-ay.
43. If x'-' (x +y + z)= (y) = then will
y.
m (X +y+Z)= -px- qy.
44. If =ea f (x - y), then will a (p + q) =
45. If Z22=x2+ (-), then will px +- qy z= 2.
46. If z = e yf(x + y), then will (p - q) (x + y) z,
47. If sin' -1 =log - (y2 + 2), then will
/y2 + z2
px +qz + y= o.
48. If = tl.f (;' ), then we shall have
dz
dt
49. If (m - 1)4- = XI' (, -) 9 then will
+ t I y +t+ t )
t
50. If = ( -y)2 ( + y + t), (x _ t)2 (X + y + t)
then will p (t + y) + q (t + x) + v (- + y) = o
51. If y +t= y t ( =y (x — Z y), (xy - xt)}, then
will p +q ( +t) + ( - +y)= t+y.