MATH 125 Quiz: MATH 125 UWashington Quiz125W13 ans

• School: UW
• Department: Mathematics
• Course: MATH 125
• Professor: All

Document Summary

Mathematical economics exam #2, november 4, 2014: consider the function f(t) = (cid:20) t2. T(cid:21): compute the tangent vector of f at any t, give an equation for the tangent line at the point (cid:20) 4. Answer: the tangent vector is given by the derivative df dt. 1(cid:21) : the point is f(2), so the tangent vector is (cid:20) 4 the tangent line. L =(cid:12)(cid:20) x y(cid:21) : (cid:20) x y(cid:21) = (cid:20) 4. It can also be written by eliminating t from the equations. For that, y = 2 t: let f : r2 so t = (2 + y). Substituting in x = 4 + 4t yields 4 = x + 4y. Answer: the level curves are {(x, y) r2, we examine whether f. + : x2/3y1/3 = q} for q 0. Y = (1/3)x2/3y 2/3 6= 0 for x, y 6= 0. This condition is satis ed since x2/3y1/3 = q > 0.