## Question

###### Evaluate the integralL" [ (- 1) min(1,V) dydr, where min(T,y) is the minimum value of and Let f,9 : R+ Rbe functions of one variable such that f" aId 9" are continuous_ Show that L Kco) 9" (y)) dyds f(0) 9(0) f(2) 9(2) + 2f' (2) "24 (0) . Let a > 0 In spherical coordinates. surface defined by r = 2acos for 0 < 0< 3 Find the volume of the solid enclosed by the surface, #S function of a Consider the inner product space P(R) with inner product(p. 4)p(r)alz) dr

Evaluate the integral L" [ (- 1) min(1,V) dydr, where min(T,y) is the minimum value of and Let f,9 : R+ Rbe functions of one variable such that f" aId 9" are continuous_ Show that L Kco) 9" (y)) dyds f(0) 9(0) f(2) 9(2) + 2f' (2) "24 (0) . Let a > 0 In spherical coordinates. surface defined by r = 2acos for 0 < 0< 3 Find the volume of the solid enclosed by the surface, #S function of a Consider the inner product space P(R) with inner product (p. 4) p(r)alz) dr Vp,q â‚¬ P(R)_ Use the Gram-Schmidt process t0 construct orthonormal lutsis from the basis {LI,I} vOUI answer t0 part (a) . give the least sqpuares approximation in P(R) to the Using function f(c) on the interial [o. 1] (Hint: You may use the following result without proof: for n =1,2 ) 1& (-1)"(&xe n); where ao = Evaluate the integral L6 [ cosh(r") dr dy dz. and between che planes and Consider the solid inside the cylinder the centre of MLASX of the solid, 14 Let the density be given by p(I V:) Fiud