Chapter 14: Q. 28 (page 883)

In Problems 7– 42, find each limit algebraically.
$\lim_{x \to - 1} {(2 x + 1)}^{5 / 3} .$

Short Answer

Expert verified

The answer is -1.

Step by step solution

Step. 1 Given Information

Given is the limit on which x tends to -1 and the function given is:

${(2 x + 3)}^{5 / 3}$

Step. 2 Solving the limit

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

Since if we put $x = - 1$ then it doesn't create any indeterminant form. So, to solve the limit we can directly put the value of x in the function. So,

\lim_{x \to - 1} {(2 x + 1)}^{5 / 3} = {(2 (- 1) + 1)}^{5 / 3} = {(- 2 + 1)}^{5 / 3} = {(- 1)}^{5 / 3} = {({(- 1)}^{1 / 3})}^{5} = {(- 1)}^{5} = - 1 .

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In Problems 7– 42, find each limit algebraically.
$\lim_{x \to - 1} {(2 x + 1)}^{5 / 3} .$

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Solving the limit

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Short Answer

Step by step solution

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In Problems 7– 42, find each limit algebraically.
$\lim_{x \to - 1} {(2 x + 1)}^{5 / 3} .$