Calculus 3

planning 11: Functions of Several Variables I Name cod on Tuesday, in class. pick out your solutions (work and answers) on this scalawag only! Let z = f (x, y ) = 4 ? x2 ? y 2 . (1) sketch the graph of the rifle. (Hint: ?rst square twain sides, like in class) (2) go back and sketch the cast off of f . (3) recover and sketch the contours f (x, y ) = c for c = ?1, 0, 2, 4, 5, if they exist. (4) Find and sketch the domain of g (x, y ) = ln(4 ? x2 ? y 2 ). 11 Homework 12: Multivariable Functions II: Limits and Continuity Name referable on Tuesday, in class. generate your solutions (work and answers) on this page only! (1) Find lim(x,y)?(1,3) (2) Find lim (x,y)?(1,1) x =y (3) Find lim (x,y)?(2,0) 2x?y =4 xy . x2 +y 2 x2 ?y 2 x?y (hint: factor) ? 2x?y ?2 2x?y ?4 (4) Show that lim(x,y)?(0,0) and C3 {y = x2 }. (hint: conjugate) 2x4 ?3y 2 x4 +y 2 (5) Show that lim(x,y)?(0,0) cos does not exist by ?nding the l imit along the three paths: C1 {x = 0}, C2 {y = 0} 2x4 y x4 +y 4 =1 12 Homework 13: Multivariable Functions III: Partial Derivatives Name Due at the beginning of our abutting class period. Submit your solutions (work and answers) on this page only!

(1) look all ?rst and second take care partial derivatives of f (x, y ) = x3 y 4 + ln( x ). y (2) Find the compare of the burn plane to the graph of the function z = f (x, y ) = exp(1 ? x2 + y 2 ) at (x, y ) = (0, 0). Convert to regulation form. (3) Find the equivalence of the tangent plane to the surface r(u, v ) = u3 ? v 3 , u + v +1, u2 at (u, v ) = (2, 1). Conv ert to universal form. (4) Suppose that! fx (x, y ) = 6xy + y 2 and fy (x, y ) = 3x2 + 2xy . see fxy and fyx to determine if there is a function f (x, y ) with these ?rst derivatives. If so, shuffle to ?nd such a function. (5) Show that the function u(x, y ) = ln( x2 + y 2 ) is Harmonic (i.e., it satis?es Laplaces equation uxx + uyy = 0). 13 Homework 14: Multivariable Functions...If you want to get a full essay, order it on our website: BestEssayCheap.com

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