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Math
Calculus
Calculus, Early Transcendentals
Chapter 14.4, Problem 1AP
Chapter 14.4, Problem 1AP
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
expand_less
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
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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
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Problem 1E: The graph of a function f is shown. Find an equation of the tangent plane to the surface z=f(x,y) at...
Problem 2E: The graph of a function f is shown. Find an equation of the tangent plane to the surface z=f(x,y) at...
Problem 3E: Find an equation of the tangent plane to the given surface at the specified point. 1. z = 2x2 + y2 ...
Problem 4E: Find an equation of the tangent plane to the given surface at the specified point. 2. z = (x + 2)2 ...
Problem 5E: Find an equation of the tangent plane to the given surface at the specified point. 3. z = exy, (2,...
Problem 6E: Find an equation of the tangent plane to the given surface at the specified point. 6. z=y2ex,(0,3,9)
Problem 7E: Find an equation of the tangent plane to the given surface at the specified point. 7. z=2y/x,(1,1,2)
Problem 8E: Find an equation of the tangent plane to the given surface at the specified point. 4. z = x/y2, (4,...
Problem 9E: Find an equation of the tangent plane to the given surface at the specified point. 5. z = x sin(x +...
Problem 10E: Find an equation of the tangent plane to the given surface at the specified point. 6. z = ln(x 2y),...
Problem 11E: Graph the surface and the tangent plane at the given point. (Choose the domain and viewpoint so that...
Problem 12E: Graph the surface and the tangent plane at the given point. (Choose the domain and viewpoint so that...
Problem 13E
Problem 14E
Problem 15E: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of...
Problem 16E: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of...
Problem 17E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)...
Problem 18E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)...
Problem 19E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)...
Problem 20E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)...
Problem 21E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)...
Problem 22E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)...
Problem 23E: Verify the linear approximation at (0, 0). 17. ex cos(xy) x + 1
Problem 24E: Verify the linear approximation at (0, 0). 18. y1x+1x+y1
Problem 25E: Given that f is a differentiable function with f(2, 5) = 6, fx(2, 5) = 1, and fy(2, 5) = -1, use a...
Problem 26E: Find the linear approximation of the function f(x, y) = 1 xy cos y at (1, 1) and use it to...
Problem 27E: Find the linear approximation of the function f(x,y,z)=x2+y2+z2 at (3, 2, 6) and use it to...
Problem 28E: The wave heights h in the open sea depend on the speed v of the wind and the length of time t that...
Problem 29E: Use the table in Example 3 to find a linear approximation to the heat index function when the...
Problem 30E: The wind-chill index W is the perceived temperature when the actual temperature is T and the wind...
Problem 31E: Find the differential of the function. 27. m = p5q3
Problem 32E: Find the differential of the function. 35. H=x2y4+y3z5
Problem 33E: Find the differential of the function. 25. z = e2x cos 2t
Problem 34E: Find the differential of the function. 26. u=x2+3y2
Problem 35E: Find the differential of the function. 35. H=x2y4+y3z5
Problem 36E: Find the differential of the function. 36. w=xzey2z2
Problem 37E: Find the differential of the function. 29. R = 2 cos
Problem 38E: Find the differential of the function. 28. T=v1+uvw
Problem 39E: If z = 5x2 + y2 and (x, y) changes from (1, 2) to (1.05, 2.1), compare the values of z and dz.
Problem 40E: If z = x2 xy + 3y2 and (x, y) changes from (3, 1) to (2.96, 0.95), compare the values of z and dz.
Problem 41E: The length and width of a rectangle are measured as 30 cm and 24 cm, respectively, with an error in...
Problem 42E: Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and...
Problem 43E: Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12...
Problem 44E
Problem 45E: The radius of a right circular cylinder is measured as 2.5ft , and the height is measured as 12ft ....
Problem 46E: The wind-chill index is modeled by the function W=13.12+0.6215T11.37v0.16+0.3965Tv0.16 where T is...
Problem 47E
Problem 48E: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =...
Problem 49E: If R is the total resistance of three resistors, connected in parallel, with resistances R1, R2 R3...
Problem 50E: A model for the surface area of a human body is given by S = 0.1091w0.425h0.725, where w is the...
Problem 51E
Problem 52E: Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1,3). You...
Problem 53E: Prove that if f is a function of two variables that is differentiable at (a,b) , then f is...
Problem 54E: (a) The function f(x,y)=xyx2+y2if(x,y)(0,0)0if(x,y)=(0,0) was graphed in Figure 4. Show that fx(0,0)...
Problem 1AP
Problem 2AP
Problem 3AP
Problem 4AP
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