Explanation Given information: f ( x , y ) = { x 2 + y 2 i f x 2 + y 2 < 1 1 i f x 2 + y 2 ≥ 1 Concept used: If the function is continuous the left hand limit and right limit of the function must be equal. Calculation: To find whether the function is continuous or not we will find left hand limit and right hand limit along x and y axis. We know that along x -axis, y = 0 f ( x , 0 ) = x 2 + 0 2 = x 2 For left hand limit, x = 1 − h and since x → 1 , h → 0 lim x → 1 f ( x , 0 ) = lim x → 1 x 2 = lim h → 0 ( 1 − h ) 2 = lim h → 0 ( 1 − 2 h + h 2 ) = 1 ... ( 1 ) For right hand limit, x = 1 + h and since x → 1 , h → 0 lim x → 1 f ( x , 0 ) = lim x → 1 x 2 = lim h → 0 ( 1 + h ) 2 = lim h → 0 ( 1 + 2 h + h 2 ) = 1

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

4th Edition

ISBN: 9781319057664

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.2, Problem 47E

To determine

Tofind:

Whether the function continuous.

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Chapter 14.2, Problem 46E

Chapter 14.2, Problem 48E

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Chapter 14 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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Tofind: Whether the function continuous.

Solution Summary: The author explains that if the function is continuous, the left hand and right hand limit must be equal.