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Chapter 11: Q. 5 (page 901)

Finding limits: Find the given limits if they exist. If a limit does not exist, explain why.

limt鈫�0鈥�1/(3+t)鈭�1/3t,(3+t)2鈭�9t

Short Answer

Expert verified

limt鈫�0鈥�1/(3+t)鈭�1/3t,(3+t)2鈭�9t=-19,6

Step by step solution

01

Step 1. Given information

limt鈫�0鈥�1/(3+t)鈭�1/3t,(3+t)2鈭�9t

02

Step 2. Finding limit for limt→0 1/(3+t)−1/3t

limt鈫�0鈥�1/(3+t)鈭�1/3t=鈭�13(t+3)

limt鈫�0鈥�1/(3+t)鈭�1/3t=-13(0+3)

limt鈫�0鈥�1/(3+t)鈭�1/3t=-19

03

Step 3. Finding limit for limt→0 (3+t)2−9t

limt鈫�0鈥�(3+t)2鈭�9t=limt鈫�0鈥�t+6

limt鈫�0鈥�(3+t)2鈭�9t=0+6=6

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