find the limit. if in doubt, look at the functions graph.\nlim cos^{-1}x\nx→-1^{+}\nlim cos^{-1}x = (type an…

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

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

Answer

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)