f. Shown below in Figure 10.1.11 is a set of contour lines of the function f. What is the behavior of f(x, y) as (x, y) approaches (0,0) along any straight line? How does this observation reinforce your conclusion about the existence of lim(z)+(0,0) f(x, y) from the previous part of this activ- ity? (Hint: Use the fact that a non-vertical line has equation y = mz for some constant m.) Figure 10.1.11 Contour lines of f(x,y)=√√²+²
f. Shown below in Figure 10.1.11 is a set of contour lines of the function f. What is the behavior of f(x, y) as (x, y) approaches (0,0) along any straight line? How does this observation reinforce your conclusion about the existence of lim(z)+(0,0) f(x, y) from the previous part of this activ- ity? (Hint: Use the fact that a non-vertical line has equation y = mz for some constant m.) Figure 10.1.11 Contour lines of f(x,y)=√√²+²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I only need help with f. The others are for reference.
Transcribed Image Text:CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS
d. What is the behavior of f along the line yz when z>0; that is, what
is the value of f(x, a) when z>07 If we approach (0,0) by moving along
the line y in the first quadrant (thus considering f(z, z) as z 0,
what value do we find as the limit?
52
o. In general, if lim(.)-(0,0) f(x, y) = L, then f(x, y) approaches L as (x, y)
approaches (0,0), regardless of the path we take in letting (z,y) → (0,0).
Explain what the last two parts of this activity imply about the existence
of lim(z.)-(0,0) f(z, v).
f. Shown below in Figure 10.1.11 is a set of contour lines of the function
f. What is the behavior of f(x, y) as (x, y) approaches (0,0) along any
straight line? How does this observation reinforce your conclusion about
the existence of lim(z,y) (0,0) f(x, y) from the previous part of this activ-
ity? (Hint: Use the fact that a non-vertical line has equation y = mz for
some constant m.)
Figure 10.1.11 Contour lines of f(x,y)=√√²+²
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