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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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.

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

(b)

To determine

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

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