f (x, y) is a differentiable function with Vf(4,3) = 7i+ 5j. 2. Suppose w = (a) Find the directional derivative of f at the point (4, 3) in the direction of the vector 3i + 2j. (b) For w = f(x, y), x = 6s tan? (t) and y = s2 + 10 sin(t), find Ət |(s,t)=(2,7/6)

Consider the following. Function: h(x, y) 9у cos (x - у) Point: (0, ) 3. (a) Find the gradient of the function. -9y sin(x - y) i + 9 cos(x - y) + 9y sin(x – y) j (b) Find the maximum value of the directional derivative at the given point. (Give your answer correct to 2 decimal places.)

1 (a) Find the point that is a distance 0.1 from the point P = (3,5) in the direction of v = (3,-1). Give five decimal places in your answer. Q = ( (b) Use P and Q to approximate the directional derivative of f(x, y) = √√x+3y at P, in the direction of v. f.≈ (c) Give the exact value for the directional derivative you estimated in part (b). fv