Calendar: 1860-1861 Page 482

GENERAL LITERATURE AND SCIENCE 483 III -Stffronttal Calculus Differentiate the following functions xn -n log" Vl xn tan -1 &3 i2' Expand sin-1 -f and tan χ according to the powers of Expand e" cos χ to four terms and show that jr4 "in tf χ---I----- &c Find values of χ which make maximum when χ -f- xe sin χ sin Inscribe the greatest rectangle in an ellipse י χ tan χ Find the value of -- when χ cos χ cos χ log sin and of when χ Prove that if 2- iir Show that the greatest rectangle that can be drawn with its sides passing through the angles of the square Α Β CD is another square whose side is equal to the diagonal AD Draw an asymptote to the curve defined by the equation y2 2-3 Saxy find also the maximum ordinate and show that the portion of the curve which lies in the first quadrant is circumscribed by square whose area 2a2 γ 2Γ Η Η