1 Foundation For Calculus: Functions And Limits 2 Key Concept: The Derivative 3 Short-cuts To Differentiation 4 Using The Derivative 5 Key Concept: The Definite Integral 6 Constructing Antiderivatives 7 Integration 8 Using The Definite Integral 9 Sequences And Series 10 Approximating Functions Using Series 11 Differential Equations 12 Functions Of Several Variables 13 A Fundamental Tool: Vectors 14 Differentiating Functions Of Several Variables 15 Optimization: Local And Global Extrema 16 Integrating Functions Of Several Variables 17 Parameterization And Vector Fields 18 Line Integrals 19 Flux Integrals And Divergence 20 The Curl And Stokes’ Theorem 21 Parameters, Coordinates, And Integrals expand_more
14.1 The Partial Derivative 14.2 Computing Partial Derivatives Algebraically 14.3 Local Linearity And The Differential 14.4 Gradients And Directional Derivatives In The Plane 14.5 Gradients And Directional Derivatives In Space 14.6 The Chain Rule 14.7 Second-order Partial Derivatives 14.8 Differentiability Chapter Questions expand_more
Problem 1E: In Exercises 18, nd the equation of the tangent plane at the given point. z=yex/y at the point (1,... Problem 2E: In Exercises 18, nd the equation of the tangent plane at the given point. z=sin(x,y) at x = 2, y =... Problem 3E: In Exercises 18, nd the equation of the tangent plane at the given point. z=ln(x2+1)+y2 at the point... Problem 4E Problem 5E Problem 6E: In Exercises 18, nd the equation of the tangent plane at the given point. x2+y2z=1 at the point (1,... Problem 7E Problem 8E: In Exercises 18, nd the equation of the tangent plane at the given point. x2y+ln(xy)+z=6 at the... Problem 9E Problem 10E Problem 11E: In Exercises 912, nd the dierential of the function. z=excosy Problem 12E: In Exercises 912, nd the dierential of the function. h(x,t)=e3tsin(x+5t) Problem 13E: In Exercises 1316, nd the dierential of the function at the point. g(x,t)=x2sin(2t) at (2, /4) Problem 14E Problem 15E Problem 16E: In Exercises 1316, nd the dierential of the function at the point. F(m, r) = Gmr2 at (100, 10) Problem 17E Problem 18E: In Exercises 1720, assume points P and Q are close. Estimate f = f(Q) f(P ) using the dierential... Problem 19E: In Exercises 1720, assume points P and Q are close. Estimate f = f(Q) f(P) using the dierential... Problem 20E: In Exercises 1720, assume points P and Q are close. Estimate f = f(Q) f(P ) using the dierential... Problem 21E Problem 22E Problem 23E Problem 24E: In Exercises 2124, assume points P and Q are close. Estimate g(Q).... Problem 25E Problem 26E Problem 27E Problem 28E Problem 29E: The tangent plane to z = f(x, y) at the point (1, 2) is z = 3x + 2y 5. (a). Find fx(1, 2) and.... Problem 30E: Find an equation for the tangent plane to z = f(x, y) at (3, 2) if the dierential at (3, 2) is df =... Problem 31E Problem 32E Problem 33E Problem 34E: (a). Find the equation of the plane tangent to the graph of f(x,y)=x2exy at (1, 0). (b). Find the... Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E format_list_bulleted