To determine To calculate: The value of limit, lim x → 2 x 2 − 5 x + 6 x 2 − 6 x + 8 . Explanation Given: The function, f ( x ) = x 2 − 5 x + 6 x 2 − 6 x + 8 . 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 − 5 x + 6 x 2 − 6 x + 8 can be found out by 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 − 6 x + 8 ) = 0 , 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 − 5 x + 6 x 2 − 6 x + 8 = lim x → 2 x 2 − 3 x − 2 x + 6 x 2 − 4 x − 2 x + 8 = lim x ș

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Chapter 11.1, Problem 39E

To determine

To calculate: The value of limit, limx→2x2−5x+6x2−6x+8.

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Chapter 11.1, Problem 38E

Chapter 11.1, Problem 40E

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