Calendar: 1849-1850 Page 292

290 APPLIED SCIENCES 10 Integrate fti cos rr cos cos ρ χ dx and χ Χξ χ2 tan -1 dx 11 If Ρ Τ be tangent to parabola at given point and Τ any other tangent the angle Τ is constant mn tan χ 12 Prove -- ψϊΤΖΓΤΡ 25 π5 13 Given the base and altitude of pyramid construct it so as to have the least surface 14 If ζ α χ φ ax eliminate the arbitrary functions II -Differential anil irnteijval £aleulusi If Ρ be the chord of an arc of the logarithmic spiral Ρ Τ Τ two tangents and the pole then ST PQ SP PT SQ Find the value of ilt Hnr s1-0 wheajL- λ 2זג cot a-- when χ צ γ If in spirals the perpendicular on the tangent show that Ρ ι η' ηβ Ex cos Given the base of triangle lind the locus of the vertex when the exterior angle is three times the inteiior and opposite angle Trace the curve draw its asymptote and find the area