QUESTION 1 Suppose that = = ceos(y) -y", y =s+t-1, x = st -12. Find 02/ds and Oz/at at the point (s, t) = (1, 0). QUESTION 2 Suppose that z = f(x, y), x = st and y = s+2. Suppose that 02/Or(x = 2, y = 5) = -4 and that Oz/dy(x = 2, y = 5) = 3. Find 02/0s and Oz/at at the point (s, t) = (1, 2). QUESTION 3 In a simple electrical circuit, the current / can be expressed as a function of the resistance R and the voltage V by I(R. V) = V/R. At a certain time, the resistance is 150 and the voltage is 0.6. At that specific time, dR/dt = -0.1 and dV/dt = 0.03. Find the rate of change of the current at that time. QUESTION 4 Assume & is implicitly defined as a function of c and y by the equation x2 - 12 - 23 = 0 Find Oz/Or and 02/dy at the point (5,3, -4). QUESTION 5 Let f(x, y) = 3 erdt. Find f, and fy- Hint: Use the Fundamental Theorem of Calculus and the Chain Rule. QUESTION 6 Let f(I, y ) = Pty (a). Find the gradient of f at the point where (c, y) = (1, 2). (b). Find the directional derivative of f at the point where (c, y) = (1, 2) in the direction of the vector . Hint: Find a unit vector in the same direction -3 > first