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Chapter 12: Q. 5 (page 989)

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

lim(x,y)鈫�(1,2)x2+y2x2-y2

Short Answer

Expert verified

lim(x,y)鈫�(1,2)x2+y2x2-y2=-53

Step by step solution

01

Step 1. Given information is:

lim(x,y)鈫�(1,2)x2+y2x2-y2

02

Step 2. Evaluating Limits

Sinceas(x,y)鈫�(1,2),x2+y2=12+22=5,x2-y2=12-22=-3lim(x,y)鈫�(1,2)x2+y2x2-y2=5-3=-53Hence,lim(x,y)鈫�(1,2)x2+y2x2-y2=-53

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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)=xywhenx2+4y2=16

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)=xywhenx2+y2=16

Letz=(f(x,y))n.Showthat鈭�z鈭�x=n(f(x,y))n-1鈭�f鈭�xand鈭�z鈭�y=n(f(x,y))n-1鈭�f鈭�y.

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f(x,y,z)=xyz,P=(2,3,1),v=鉄�2,1,鈭�2鉄�

Explain how you could use the method of Lagrange multipliers to find the extrema of a function of two variables, f(x,y),subject to the constraint that (x,y)is on the boundary of the rectangle Rdefined bya鈮�x鈮�bandc鈮�y鈮�d.
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