Chapter 14.2, Problem 24AYU

To determine

To find: The value of the given limit.

Answer to Problem 24AYU

The value of the limit is $1$ .

Explanation of Solution

Given:

The given limit is $\underset{x\to 0}{\lim }\sqrt{1-2x}$

Calculation:

Consider the given limit is,

  $\underset{x\to 0}{\lim }\sqrt{1-2x}$

Consider the function as,

  $\underset{x\to c}{\lim }\sqrt[n]{f\left(x\right)}=\sqrt[n]{\underset{x\to c}{\lim }f\left(x\right)}$

Then,

  $\begin{array}{c}\underset{x\to 0}{\lim }\sqrt{1-2x}=\underset{x\to 0}{\lim }\sqrt{1-2x}\\ =\sqrt{\underset{x\to 0}{\lim }1-\underset{x\to 0}{\lim }2x}\\ =\sqrt{1-2\underset{x\to 0}{\lim }x}\\ =1\end{array}$