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Chapter 3: Q. 10 (page 310)

Each of the limits in Exercises 7鈥�12 is of the indeterminate form 0路鈭�or 鈭�路0. Rewrite each limit so that it is (a) in the form 00and then (b) in the form 鈭�鈭�. Then (c) determine which of these indeterminate forms would be easier to work with when applying L鈥橦opital鈥檚 rule.

10.limx鈫�0x3lnx

Short Answer

Expert verified

Part (a) The limit in the form 00is localid="1648575908433" limx鈫�0x31lnx

Part (b) The limit in the form 鈭�鈭�is limx鈫�0lnx1x3

Part (c) Part (b) is easier to work with L'Hospital's rule.

Step by step solution

01

Part (a) Step 1. Given information

We have been given the limitlimx鈫�0x3lnx

02

Part (a) Step 2. Write the limit in the form 00

limx鈫�0x3lnx=limx鈫�0x31lnx

03

Part (b) Step 1. Write the limit in the form ∞∞

limx鈫�0x3lnx=limx鈫�0lnx1x3

04

Part (c) Step 1. Determine which of these indeterminate forms would be easier to work with when applying L’Hopital’s rule.

limx鈫�0x3lnx=limx鈫�0lnx1x3=limx鈫�01x-3x-4=limx鈫�0-13x3=0

Therefore, part (b) is easier to work with L'Hospital's rule.

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