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Chapter 12: Q. 4 (page 988)

Describe the meanings of each of the following mathematical expressions:
$D_{u} f (x_{0}, y_{0})$

Short Answer

Expert verified

Ans: $D_{u} f (x_{0}, y_{0})$ It means derivative of a function $f$ at a point $(x_{0}, y_{0})$ with respect to $u$ .

Step by step solution

Step 1. Given information.

given,

$D_{u} f (x_{0}, y_{0})$

Step 2. Meaning is,

$D_{u} f (x_{0}, y_{0})$ it means derivative of a function $f$ at a point $(x_{0}, y_{0})$ with respect to $u$ .

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Most popular questions from this chapter

In Exercises $37 - 42$ , use the partial derivatives of role="math" localid="1650186853142" $g (x, y) = \tan^{- 1} (x y^{2})$ and the point role="math" localid="1650186870407" $(1, 0)$ specified to

$(a)$ find the equation of the line tangent to the surface defined by the function in the $x$ direction,

$(b)$ find the equation of the line tangent to the surface defined by the function in the $y$ direction, and

$(c)$ find the equation of the plane containing the lines you found in parts $(a)$ and $(b)$ .

Describe the meanings of each of the following mathematical expressions :

$\frac{\partial w}{\partial y}$

$A chain rule for functions of two variables : Let f (x, y) = x^{2} y^{3}, x = s \cos t, and y = s \sin t . Find \frac{\partial f}{\partial x} and \frac{\partial f}{\partial y} .$

Sketch the level curves f(x, y) = c of the following functions for c = −3, −2, −1, 0, 1, 2, and 3:

$f (x, y) = x - \sin^{- 1} y$

Evaluate the following limits, or explain why the limit does not exist.

$\lim_{(x, y, z) \to (0, 0, 0)} \frac{x^{2} + y^{2}}{x^{2} + y^{2} + z^{2}}$

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Describe the meanings of each of the following mathematical expressions: Dufx0,y0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Meaning is,

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Most popular questions from this chapter

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Describe the meanings of each of the following mathematical expressions:
$D_{u} f (x_{0}, y_{0})$