 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 20837 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 and is associated to the ISBN: 9780538497879.

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Compounded annually
See Compounded k times per year.

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

End behavior
The behavior of a graph of a function as.

Frequency
Reciprocal of the period of a sinusoid.

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Infinite limit
A special case of a limit that does not exist.

Inverse function
The inverse relation of a onetoone function.

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Onetoone rule of exponents
x = y if and only if bx = by.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Radicand
See Radical.

Rational expression
An expression that can be written as a ratio of two polynomials.

Regression model
An equation found by regression and which can be used to predict unknown values.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Standard deviation
A measure of how a data set is spread

Unbounded interval
An interval that extends to ? or ? (or both).

xaxis
Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.