Chapter 11, Problem 21RE

To determine

To calculate:

The limit by using the substitution method:

  $\underset{x\to 0}{\lim }\arccos x$

Answer to Problem 21RE

By using the substitution method, $\underset{x\to 0}{\lim }\arccos x$ is $\frac{\pi }{2}$ .

Explanation of Solution

Given information:

  $\underset{x\to 0}{\lim }\arccos x$

Formula Used:

If the polynomial function is represented by $p$ and its real number is $c$ then;

  $\underset{x\to 0}{\lim }p\left(x\right)=p\left(c\right)$

Calculation:

The given function is:

  $\underset{x\to 0}{\lim }\arccos x$

The limit of the given function is calculated by using the substitution method as:

Put $x=0$ :

  $\begin{array}{l}\underset{x\to 0}{\lim }\arccos \left(x\right)=\arccos \left(0\right)\\ \underset{x\to 0}{\lim }\arccos \left(x\right)=\frac{\pi }{2}\end{array}$