Calendar: 1888-1889 Page 747

ENGINEERING DEPARTMENT 739 precisely what observations should be made at and Β and what calculations should be performed in order to find the distance PQ If PQ subtend the same angle at and Β and QB subtend at and PA subtend 3a at Β prove that PQ AB sin sin 5a Walking along straight road observe two objects Β of which is the nearer in line making an angle of 30 with the road after walking mile and are in line at right angles to the road and after walking mile further BC are in line making an angle of 60 with the road Find the distances of from one another Prove that increases but not indefinitely as χ increases and assuming that it has limit find the limits ax when χ of and log Define differential coefficient and from your definition find the differential coefficients with respect to χ of x2 and xi Obtain the differential coefficients with respect to χ of sin sin τ and and differentiate x2 log tan log χ an log tan χ tan og 10 If trace the change in sign and magnitude of as χ changes from to and illustrate by diagram 11 Shew how to find the points on curve at which the tangent is parallel to either of the axes apply your method to the curve Sa 3a 12 Explain the meaning of and prove that X- ax dy If χ si a2 x2 obtain χ in terms of and verify that χ dJH dx dy