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Chapter 12: Q. 24 (page 953)

In Exercises 21-28, find the directional derivative of the given function at the specified point $P$ and in the direction of the given unit vector $\mathbf{u}$.

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Most popular questions from this chapter

In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.

$f (x, y, z) = x y z when x^{2} + y^{2} + z^{2} = 9$

$Extrema : Find the local maxima, local minima, and saddle points of the given functions f (x, y) = x^{3} - 12 xy - y^{3} .$

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

Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.

$f (x, y) = \frac{y}{x}, P = (4, 3), v = ⟨ 3, - 2 ⟩$

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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In Exercises 21-28, find the directional derivative of the given function at the specified point \(P\) and in the direction of the given unit vector \(\mathbf{u}\).

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