1. (a) For the function f(x,y) = sin(xtany), calculate control and at the point (3, 1). (b) () Calculate the following integral using polar coordinates by integrating first with re- spect to r and second with respect to e: 1= [[62 +93 ?dards where D is the interior of a closed curve: x2 + y2 = 2y. (ii) Write down the integral in (1) as repeated integrals in polar coordinates by integrating first with respect to 0 and second with respect to r. (You do not need to calculate the resulting repeated integrals.) 1 (iii) Using the result of (i), or otherwise, integrate = [] (2+x2312+y+sin(e) dedy, (iv) Evaluate the volume of one of two identical curved wedges cut out from a cylinder x2 + y2 = 2y by the planes z = 0 and z= x. 1. (a) For the function f(x,y) = sin(xtany), calculate control and at the point (3, 1). (b) () Calculate the following integral using polar coordinates by integrating first with re- spect to r and second with respect to e: 1= [[62 +93 ?dards where D is the interior of a closed curve: x2 + y2 = 2y. (ii) Write down the integral in (1) as repeated integrals in polar coordinates by integrating first with respect to 0 and second with respect to r. (You do not need to calculate the resulting repeated integrals.) 1 (iii) Using the result of (i), or otherwise, integrate = [] (2+x2312+y+sin(e) dedy, (iv) Evaluate the volume of one of two identical curved wedges cut out from a cylinder x2 + y2 = 2y by the planes z = 0 and z= x