Evaluate the limit. √x+y-3 (x,y) →(4,5) x+y-9 lim Select the correct choice below and, if necessary, fill in the answer box to complete your choice. √√x+y-3 (x,y) →(4,5) x+y-9 B. The limit does not exist. O A. lim (Simplify your answer.)

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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Question
←
Evaluate the limit.
√x+y-3
lim
(x,y) →(4,5) X+y-9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
√x +y -3
lim
(x,y) →(4,5) x+y-9
B. The limit does not exist.
O A.
...
=
(Simplify your answer.)
Transcribed Image Text:← Evaluate the limit. √x+y-3 lim (x,y) →(4,5) X+y-9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. √x +y -3 lim (x,y) →(4,5) x+y-9 B. The limit does not exist. O A. ... = (Simplify your answer.)
Expert Solution
Step 1: Finding the limit of the function

The given function is multivariable rational function, To find the limit of the given function factorized the denominator of the function, we get


limit as left parenthesis x comma y right parenthesis rightwards arrow left parenthesis 4 comma 5 right parenthesis of fraction numerator square root of x plus y end root minus 3 over denominator x plus y minus 9 end fraction equals limit as left parenthesis x comma y right parenthesis rightwards arrow left parenthesis 4 comma 5 right parenthesis of fraction numerator square root of x plus y end root minus 3 over denominator left parenthesis square root of x plus y end root right parenthesis squared minus 3 squared end fraction
equals limit as left parenthesis x comma y right parenthesis rightwards arrow left parenthesis 4 comma 5 right parenthesis of fraction numerator square root of x plus y end root minus 3 over denominator left parenthesis square root of x plus y end root minus 3 right parenthesis left parenthesis square root of x plus y end root plus 3 right parenthesis end fraction
equals limit as left parenthesis x comma y right parenthesis rightwards arrow left parenthesis 4 comma 5 right parenthesis of fraction numerator 1 over denominator left parenthesis square root of x plus y end root plus 3 right parenthesis end fraction
equals fraction numerator 1 over denominator left parenthesis square root of 4 plus 5 end root plus 3 right parenthesis end fraction
equals fraction numerator 1 over denominator left parenthesis square root of 9 plus 3 right parenthesis end fraction
equals fraction numerator 1 over denominator left parenthesis 3 plus 3 right parenthesis end fraction
equals 1 over 6

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