Explanation Given information: lim ( x , y ) → ( 0 , 0 ) ( 5 x 2 − 2 x y + y 2 + 3 ) and limit exist. Concept and Formula Used: Concept of limit: Limit of a function exists if the form is determinate i.e. 0 1 , ∞ + ∞ , 0 ⋅ ∞ etc . To find the value of limit in determinate form directly put the value of variable into it. Calculation: It is given that lim ( x , y ) → ( 0 , 0 ) ( 5 x 2 − 2 x y + y 2 + 3 ) As, the form is determinate i.e. not 0 0 therefore limit exist and putting the values of variable i.e

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ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 11.2, Problem 4PS

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To Calculate: lim(x,y)→(0,0)(5x2−2xy+y2+3)

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lim ( x , y ) → ( 0 , 0 ) ( 5 x 2 − 2 x y + y 2 + 3 )

Solution Summary: The author explains that limit exists if the form is determinate i.e. not 01, putting the values of variable into it.

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