Exam 1 with Resolution | Calculus and Analytic Geometry IV | MATH 2443, Exams of Analytical Geometry and Calculus

Download Exam 1 with Resolution | Calculus and Analytic Geometry IV | MATH 2443 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! QJ)... [10 points] Is the function 2, f(zy) = 0 (z,y) = (0,0) continuous at the point (0,0)? Give reasons for your answer. No. Len fesyy = Lin O «3 09) koe “ye alone, Ke axis 1) bio fos) = Lim x bye 4) 3¢,2) roo WK +K alana yee These dot agree => Bt (ev) # (0,0) "¢" = 3 2 ] = Las (0) <O 8 ye z C4 =hm ft) 2 4 > (4) ra Lin fy) D.NE. 4) 30°) > Frew) Not Gon Nnwovr of (ar). nae points] Let f(z, y,z) = a° + + 32°, Q2 30 poi L 24 Dy? + 32? (a) In what direction is f increasing most rapidly at the point (1,1, 1), and what is this rate of increase? Increasing Most rapidly in VE ua) diced = 2x, bys bEP Wy €2, erb ? Role ah tacreasg = = (VF wa | = (@, b b> | = avy! (b) Find the equation of the tangent plane to the surface f(x,y, z) = 6 at the point (1, 1,1). Normal = VE (ya) Porat = (ut4) a) Vln <K-t) yl) B12 = © it» +2094) + 3G@)=0 (c) What is the rate of change of f at (1, 1,1) in the direction from (1,1, 1) to (—1,0,2)? a = 10,29 = CUU) Rake Schone = Daf oss) Tew <unvl = Von a 1] 4b cov = G1, ty? NU Ve!