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Chapter 3: Q. 51 (page 311)

Calculate each of the limits in Exercises 49-64. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.

limx鈫�2+(x-2)x2-4.

Short Answer

Expert verified

The exact value of the limitlimx鈫�2+(x-2)x2-4is,1.

Step by step solution

01

Step 1. Given information

limx鈫�2+(x-2)x2-4.

02

Step 2. Taking logarithm of the limit.

limx鈫�2+ln(x-2)x2-4=limx鈫�2+x2-4ln(x-2).

=limx鈫�2+ln(x-2)x2-4 [ in the form of 鈭�鈭�]

=limx鈫�2+1(x-2)-1x2-42路2x=-limx鈫�2+1(x-2)x2-422x=-limx鈫�2+1(x-2)(x-2)2(x+2)22x=-limx鈫�2+(x-2)(x+2)22x=0

03

Step 3. Therefore, the value of the limit is given by,

limx鈫�2+ln(x-2)x2-4=e0=1

Therefore, the exact value is,1.

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Most popular questions from this chapter

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