Chapter 4.7, Problem 101E

To determine

To fill the blank if possible or state the reason.

Answer to Problem 101E

For $x\to -1^{+}$ , the value of $\arccos x\to \text{}\text{}$

  $\pi$

Explanation of Solution

Given information:

The notation $x\to c^{+}$ indicates that $x$ approaches $c$ from the right and $x\to c^{-}$ indicates that $x$ approaches $c$ from the left.

As $x\to -1^{+}$ ,the value of $\arccos x\to$ -- ----.

Calculation:

Find that as $x\to -1^{+}$ ,the value of $\arcsin x\to$ -- ----.

The domain of the function $f\left(x\right)=\arccos \left(x\right)$ is $\left[-1,1\right]$ and its range is $x\in \left[0,\pi \right]$ .

Also, the graph for the function is continuous, and hence finding the value of the function as $x\to -1^{+}$ , is equivalent to finding the value of the function at $x=-1$ .

Hence as $x\to -1^{+}$ , $\arccos x\to \pi$ .