 14.4.1: Find an equation of the tangent plane to the given surface at the s...
 14.4.2: Find an equation of the tangent plane to the given surface at the s...
 14.4.3: Find an equation of the tangent plane to the given surface at the s...
 14.4.4: Find an equation of the tangent plane to the given surface at the s...
 14.4.5: Find an equation of the tangent plane to the given surface at the s...
 14.4.6: Find an equation of the tangent plane to the given surface at the s...
 14.4.7: Graph the surface and the tangent plane at the given point. (Choose...
 14.4.8: Graph the surface and the tangent plane at the given point. (Choose...
 14.4.9: Draw the graph of and its tangent plane at the given point. (Use yo...
 14.4.10: Draw the graph of and its tangent plane at the given point. (Use yo...
 14.4.11: Explain why the function is differentiable at the given point. Then...
 14.4.12: Explain why the function is differentiable at the given point. Then...
 14.4.13: Explain why the function is differentiable at the given point. Then...
 14.4.14: Explain why the function is differentiable at the given point. Then...
 14.4.15: Explain why the function is differentiable at the given point. Then...
 14.4.16: Explain why the function is differentiable at the given point. Then...
 14.4.17: Verify the linear approximation at .
 14.4.18: Verify the linear approximation at .
 14.4.19: Given that is a differentiable function with , , and , use a linear...
 14.4.20: Find the linear approximation of the function at and use it to appr...
 14.4.21: Find the linear approximation of the function at and use it to appr...
 14.4.22: The wave heights in the open sea depend on the speed of the wind an...
 14.4.23: Use the table in Example 3 to find a linear approximation to the he...
 14.4.24: The windchill index is the perceived temperature when the actual t...
 14.4.25: Find the differential of the function.
 14.4.26: Find the differential of the function.
 14.4.27: Find the differential of the function.
 14.4.28: Find the differential of the function.
 14.4.29: Find the differential of the function.
 14.4.30: Find the differential of the function.
 14.4.31: If and changes from to compare the values of and .
 14.4.32: If and changes from to , compare the values of and .
 14.4.33: The length and width of a rectangle are measured as 30 cm and 24 cm...
 14.4.34: Use differentials to estimate the amount of metal in a closed cylin...
 14.4.35: Use differentials to estimate the amount of tin in a closed tin can...
 14.4.36: The windchill index is modeled by the function where is the temper...
 14.4.37: The tension in the string of the yoyo in the figure is where is th...
 14.4.38: The pressure, volume, and temperature of a mole of an ideal gas are...
 14.4.39: If is the total resistance of three resistors, connected in paral l...
 14.4.40: Four positive numbers, each less than 50, are rounded to the first ...
 14.4.41: A model for the surface area of a human body is given by , where is...
 14.4.42: Suppose you need to know an equation of the tangent plane to a surf...
 14.4.43: Show that the function is differentiable by finding values of and t...
 14.4.44: Show that the function is differentiable by finding values of and t...
 14.4.45: Prove that if is a function of two variables that is differentiable...
 14.4.46: (a) The function was graphed in Figure 4. Show that and both exist ...
Solutions for Chapter 14.4: TANGENT PLANES AND LINEAR APPROXIMATIONS
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 14.4: TANGENT PLANES AND LINEAR APPROXIMATIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 14.4: TANGENT PLANES AND LINEAR APPROXIMATIONS includes 46 full stepbystep solutions. Since 46 problems in chapter 14.4: TANGENT PLANES AND LINEAR APPROXIMATIONS have been answered, more than 11328 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Multivariable Calculus, was written by Patricia and is associated to the ISBN: 9780538497879.

Augmented matrix
A matrix that represents a system of equations.

Closed interval
An interval that includes its endpoints

Directed line segment
See Arrow.

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Random behavior
Behavior that is determined only by the laws of probability.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Right triangle
A triangle with a 90° angle.

Speed
The magnitude of the velocity vector, given by distance/time.

Standard representation of a vector
A representative arrow with its initial point at the origin

Terminal side of an angle
See Angle.

Union of two sets A and B
The set of all elements that belong to A or B or both.

Vertex of a cone
See Right circular cone.

Xmin
The xvalue of the left side of the viewing window,.

Zoom out
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).