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Chapter 12: Q. 15 (page 989)

Continuity: Find the set of points where the function is continuous.

f(x,y)=lnxy

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information

f(x,y)=lnxy

02

Step 2. Explanation

The given function is a logarithmic function which is defined for non-negative values only. lnxis continuous for all x鈭�(0,鈭�). Therefore, f(x,y)=lnxyis continuous for all (x, y) inR2such that x>0, y>0 or x<0, y<0

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Most popular questions from this chapter

Partial derivatives: Find all first- and second-order partial derivatives for the following functions:

f(x,y,z)=ln鈦�(x+y+z)

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x,y)=yx,P=(4,3)

Describe the meanings of each of the following mathematical expressions :

fyx0,y0

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