MATH 226 Midterm: MATH 226 2006 Winter Test 1
Document Summary
No notes, books or calculators are to be used. No credit will be given for the correct answer without the (correct) accompanying work. Use the back of the pages if you need extra space. Rules governing examinations: each candidate must be prepared to produce, upon request, a. Let z = f (x, y) be a di erentiable function on r2 such that f (1, 2) = 3, f (1. 2, 2. 3) = 3. 4 and f (0. 9, 2. 1) = 3. 2. (a) estimate. [10pt] (b) estimate the value of the directional derivative of z = f (x, y) at the point (1, 2) as you move towards the point (2, 3). Let z = f (x, y) be a di erentiable function on r2, x = (s2 + t2)/2 and y = (s2 t2)/2. X + y + z = 2, where x > 0, y > 0 and z > 0.
