1 Functions And Models 2 Limits And Derivatives 3 Differentiation Rules 4 Applications Of Differentiation 5 Integrals 6 Applications Of Integration 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Sequences, Series, And Power Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus A Numbers, Inequalities, And Absolute Values B Coordinate Geometry And Lines C Graphs Of Second-degree Equations D Trigonometry E Sigma Notation F Proofs Of Theorems G The Logarithm Defined As An Integral expand_more
14.1 Functions Of Several Variables 14.2 Limits And Continuity 14.3 Partial Derivatives 14.4 Tangent Planes And Linear Approximations 14.5 The Chain Rule 14.6 Directional Derivatives And The Gradient Vector 14.7 Maximum And Minimum Values 14.8 Lagrange Multipliers Chapter Questions expand_more
Problem 1E Problem 2E: Explain why each function is continuous or discontinuous. (a) The outdoor temperature as a function... Problem 3E Problem 4E Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E Problem 10E Problem 11E Problem 12E: Find the limit. 12. lim(x,y)(,/2)cosysin2ycosxcosy Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E: Show that the limit does not exist. 17. lim(x,y)(0,0)y2sin2xx4+y4 Problem 18E Problem 19E Problem 20E: Find the limit, if it exists, or show that the limit does not exist. 20. lim(x,y)(,1/2)exysinxy Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E: Find the limit, if it exists, or show that the limit does not exist. 27. lim(x,y,z)(6,1,2)x+zcos(y) Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E: Find h(x, y) = g(f(x, y)) and the set of points at which h is continuous. 26. g(t) = t + ln t,... Problem 39E: Graph the function and observe where it is discontinuous. Then use the formula to explain what you... Problem 40E: Graph the function and observe where it is discontinuous. Then use the formula to explain what you... Problem 41E: Determine the set of points at which the function is continuous. 29. F(x,y)=xy1+exy Problem 42E: Determine the set of points at which the function is continuous. 30. F(x,y)=cos1+xy Problem 43E: Determine the set of points at which the function is continuous. 31. F(x,y)=1+x2+y21x2y2 Problem 44E: Determine the set of points at which the function is continuous. 32. H(x,y)=ex+eyexy1 Problem 45E: Determine the set of points at which the function is continuous. 33. G(x,y)=x+1x2y2 Problem 46E: Determine the set of points at which the function is continuous. 34. G(x, y) = ln(1 + x - y) Problem 47E: Determine the set of points at which the function is continuous. 35. f(x, y, z) = arcsin(x2 + y2 +... Problem 48E Problem 49E: Determine the set of points at which the function is continuous. 37.... Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E: Prove the three special limits in (2). Problem 55E: At the beginning of this section we considered the function f(x,y)=sin(x2+y2)x2+y2 and guessed on... Problem 56E: Graph and discuss the continuity of the function f(x,y)={sinxyxyifxy01ifxy=0 Problem 57E: Let f(x,y)={0ify0oryx41if0yx4 (a) Show that f(x, y) 0 as (x, y) (0, 0) along any path through (0,... Problem 58E: Show that the function f given by f(x) = |x| is continuous on n. [Hint: Consider |x a|2 = (x a) (x... Problem 59E: If c Vn, show that the function f given by f(x) = c x is continuous on n. format_list_bulleted