MATH 201 Exam 2, Fall 2013

SASL OVA See eS aN he H.Yamani — - Please write your section number on your booklet. - Please answer each problem on the indicated page(s) of the booklet. Any part of your answer that is not written on the indicated page(s) will not be graded. - Unjustified answers will receive little or no credit. em 1 (answer on page 1 of the booklet). Prot I(x, y,z)=iIn (e? — Xe yt 2 Given (i) (8 pts Wind the domain and range of the function / . (ii) (6 pts) Determine if the domain-of f is an Gpen Fesion, a closed region, or neither and decide if the ain of f idbounded obunboun ed. 2, (answer on page 2 of the booklet) the equation of the tangent plane and normal line to the surface 2) at the point (1,1,/24). Proble (14 pts) Fi z=inl4—x? Problem 3 (answer on page 3 of the booklet) Determine if the limit of each of the following functions exists as (x, y) — (0,0). Explain (7 pts each) PRE ey? xy S ney f(x, y)= eee (i) f(x,y) Pos (ii) g(x,y) 4y —3x 2x bat Bes i a * (iii) A(x, y)= Ys 2 | Be) ae gS ai.) Proklem 4 (answer on page 4 booklet) (14 ptS}\ Find the maximum and minimum values of f (x, y)= x? + y? —x-y on Problem 5 (answer on page 5 of the booklet) . Suppose that f(x,y,z)is a differentiable function and given that 6,2,0)=-L Vf(6,2,0)=3i— J +5k, $211)=-9,V/2L1)=i- j+k 2 y=rs z=rins and w= f(x,y,z) (iii)(8 pts) Find an rmal line to the surface w(r,s) = 2t? —5in the rst -space. Problem 6 (answer on page 6 of the booklet). (6 pts) Prove that the function / (x,y)=2x+4y+x | _ the plane. < y? is differentiable everywhere in