Calculus 3

planning 11: Functions of Several Variables I Name collectible on Tuesday, in class. pick out your solutions (work and answers) on this knave only! Let z = f (x, y ) = 4 ? x2 ? y 2 . (1) sketch the graph of the place. (Hint: ?rst square some(prenominal) sides, like in class) (2) go back and sketch the value 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 payable on Tuesday, in class. carry 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 ?ndi ng the limit 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 turn back 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 comparison of the tangent plane to the surface r(u, v ) = u3 ? v 3 , u + v +1, u2 at (u, v ) = (2, 1). Convert to recipe form. (4) Suppose that f x (x, y ) = 6xy + y 2 and fy (x, y ) = 3x2 +! 2xy . hold back 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: OrderEssay.net

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