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Q, 27

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Found in: Page 883

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problems 7– 42, find each limit algebraically. $\underset{x\to 2}{\mathrm{lim}}{\left(3x-2\right)}^{5/2}$.

See the step by step solution

## Step. 1 Given Information

Given is the limit on which x tends to 2 and the function given is:

${\left(3x-2\right)}^{5/2}$

## Step. 2 Solving the limit

Firstly, we check whether the given function is in indeterminant form or not.

Since if we put $x=2$ then it doesn't create any indeterminant form. So, to solve the limit we can directly put the value of x in the function.

$\underset{x\to 2}{\mathrm{lim}}{\left(3x-2\right)}^{5/2}={\left(3\left(2\right)-2\right)}^{5/2}\phantom{\rule{0ex}{0ex}}={\left(6-2\right)}^{5/2}\phantom{\rule{0ex}{0ex}}={4}^{5/2}\phantom{\rule{0ex}{0ex}}={\left(\sqrt{4}\right)}^{5}\phantom{\rule{0ex}{0ex}}={2}^{5}=32.$