The temperature (in degree Celsius) on a metal plate, given by T(x, y) = x sin 2y

(i) What is the rate of change of T at (1.) in the direction making an angle of with the

positive x-axis?

(ii) Find the directions in which the temperature increases and decreases most rapidly at (1,5).

(iii) Find the directions in which the rate of change of T at (1.) is equal to 0?