Question

find the limit. if in doubt, look at the functions graph.
lim cos^{-1}x
x→-1^{+}
lim cos^{-1}x = (type an exact answer.)
x→-1^{+}

Explanation:

Step1: Recall the domain and range of \(y = \cos^{-1}x\)

The domain of \(y=\cos^{-1}x\) is \([- 1,1]\) and the range is \([0,\pi]\).

Step2: Analyze the limit as \(x\to - 1^{+}\)

As \(x\) approaches \(-1\) from the right (\(x\to - 1^{+}\)), we use the fact that \(\cos(\pi)=-1\). By the definition of the inverse - cosine function \(y = \cos^{-1}x\) (where \(y\in[0,\pi]\) and \(x=\cos y\)), when \(x\to - 1^{+}\), \(y=\cos^{-1}x\to\pi\).

Answer:

\(\pi\)