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Chapter 12: Q. 15 (page 989)

Continuity: Find the set of points where the function is continuous.
$f (x, y) = \ln x y$

Short Answer

Expert verified

Points where the function is continuous are x>0, y>0 or x<0, y<0

Step by step solution

Step 1. Given information

$f (x, y) = \ln x y$

Step 2. Explanation

The given function is a logarithmic function which is defined for non-negative values only. $\ln x$ is continuous for all $x \in (0, \infty)$ . Therefore, $f (x, y) = \ln x y$ is continuous for all (x, y) in $R^{2}$ such that x>0, y>0 or x<0, y<0

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Most popular questions from this chapter

Solve the exact differential equations in Exercises 63–66. $y \cos (x y) - 3 + (x \cos (x y) + 2) \frac{d y}{d x} = 0 .$

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$Let z = f (x, y) g (x, y) . Show that \frac{\partial z}{\partial x} = \frac{f_{x} (x, y) g (x, y) - f (x, y) g_{x} (x, y)}{(g {(x, y))}^{2}} and \frac{\partial z}{\partial y} = \frac{f_{y} (x, y) g (x, y) - f (x, y) g_{y} (x, y)}{(g {(x, y))}^{2}}$

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Continuity: Find the set of points where the function is continuous.f(x,y)=lnxy

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Most popular questions from this chapter

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Continuity: Find the set of points where the function is continuous.
$f (x, y) = \ln x y$