To determine To calculate: The value of limit, lim x → − 2 x 2 + 3 x + 2 x 2 − x − 6 by using algebraic properties and properties of limits. Explanation Given: The function, f ( x ) = x 2 + 3 x + 2 x 2 − x − 6 . Formula used: lim x → a f ( x ) g ( x ) = lim x → a f ( x ) lim x → a g ( x ) Calculation: The value of lim x → − 2 x 2 + 3 x + 2 x 2 − x − 6 can be found by the application of the polynomial limit which is lim x → a f ( x ) = f ( a ) . Here, the quotient rule cannot be applied as lim x → − 2 ( x 2 − x − 6 ) = 0 , thus an irregularity is created in the limit. In this, the value of x shall be replaced by the limit that is -2. First, convert the limit into a simpler form to remove the irregularity: lim x → − 2 x 2 + 3 x + 2 x 2 − x − 6 = lim x → − 2 x 2 + x + 2 x + 6 x 2 − 3 x + 2 x − 6 = lim x → − 2 ( x + 1 ) ( x + 2 )

12th Edition

ISBN: 9780135904282

Author: Lial, HUNGERFO

Publisher: PEARSON

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Chapter 11.1, Problem 40E

To determine

To calculate: The value of limit, limx→−2x2+3x+2x2−x−6 by using algebraic properties and properties of limits.

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Chapter 11.1, Problem 39E

Chapter 11.1, Problem 41E

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