Calendar: 1854-1855 Page 352

354 GENERAL LITERATURE AND SCIENCE X- 2a Show that χ 7r sin has both maximurc χ and minimum value and distinguish between them Prove Lagrange's Theorem and expand by it in terms of when χ '-f- sin The complement of the angle tan -1 χ may be expresse by the series- 11 11 11 rr 577 &C' The area of the greatest isosceles triangle that can be described about an ellipse with its unequal side parallel to the major axis area of the ellipse 7r If it distance between two points in space and prove that d2 d-u d2 tx 7p J7 rectangular tank open at the top is to be made of given quantity of material find its form that it may contain the greatest quantity Find the radius of curvature and evolute of the catenary dy -- where ss and χ c2 α χ V- 10 Trace θ draw the rectangular and circular asymptotes and find the point of contrary flexure 11 The curve defined by ay χ -" ax has nodus of which the area is in- 'l am λ 'ό 12 Prove the following rule for finding the area of curve by means of equidistant ordinate To the sum of the first and last ordinates add four times the sum of the even and twice the sum of the odd ones and multiply by -d of the distance between each ordinate ο