   Chapter 1.6, Problem 10E

Chapter
Section
Textbook Problem

(a) What is wrong with the following equation? x 2 + x − 6 x − 2 = x + 3 (b) In view of part (a), explain why the equation lim x → 2 x 2 + x − 6 x − 2 = lim x → 2 ( x + 3 ) is correct.

(a)

To determine

To explain: The equation x2+x6x2=x+3 is incorrect.

Explanation

Let the function f(x)=x2+x6x2 and g(x)=x+3.

Construct the table of f(x) and g(x) for some arbitrary values of x.

 x f(x) g(x) −3 f(−3)=(−3)2+(−3)−6(−3)−2=0 g(−3)=−3+3=0 −2 f(−2)=(−2)2+(−2)−6(−2)−2=1 g(−2)=−2+3=1 −1 f(−1)=(−1)2+(−1)−6(−1)−2=2 g(−1)=−1+3=2 0 f(0)=(0)2+(0)−6(0)−2=3 g(0)=0+<

(b)

To determine

To explain: The equation limx2x2+x6x2=limx2(x+3) is correct.

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