Kindly help to provide working solutions as I have difficulties to solve all of the questions . Appreciate for the guidance , and thank you

1 . A right circular cylinder is inscribed in a cone with height h and base radius 1-. Find the largest possible volume of such a cylinder. . Use Newton's method to nd the absolute maximum value (up to 6 decimal places) of the function f(:r:)=.7:cos:c, US$511: . Express the following as a denite integral 1-01 f (11:) d3: and nd its value. lim n 24 i ,1st {an2 - i=1 _ Evaluate the following integrals 1:2 d:L' (a) 2 $6 33.73 + 2 1 f2 1 (h) / 1+msad9- . Let R be the region bounded by the curve y = sin (3:2) , .1; = 0, a: = J1? and the :vaxis- Find the volume when R is rotated 221* radians about the yaxis