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Q. 36

Found in: Page 120


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx3 x4 .

The limit exists and it is equal to 81.

See the step by step solution

Step by Step Solution

Step 1. Given Information.

Given:limx3 x4

Step 2. Theorem 1.16

Power functions are continuous on their domains. In terms of limits, if A is real and k is rational, then for all values x = c at which xk is defined we have limxc Axk = Ack.

Step 3. Finding limit of given function.

Using the above theorem,A = 1, c=3 and k=4.So, putting these values we get our limit as:limx3 x4 =34 = 81.

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