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Determine where f is continuous:

1. f(x) = sin-1 (2x)

2. f(x) = (sqrt(arctanx)) / (x^2 - 9)

 

I used a graphing calculator for #1 and found the interval to be [-0.5, 0.5], but is there any way I can do this more algebraically without the use of my graphing calculator?

 

I don't know how to approach #2 at all...

 

Thanks so much!

 Jun 10, 2022
 #1
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Determine where f is continuous:

 

Hello Guest!

 

1. f(x) = sin-1 (2x)\(f(x)=sin^{-1}(2x)\)

    f(x) is continuous if:   \(\color{blue}x\in \mathbb R\ |\ x\notin \{n\cdot \pi /2\}.\)

2. \(f(x) = \sqrt{arctan\ x} / (x^2 - 9)\)

   \(\sqrt{arctan\ x}/(x^2-9)\)  is continuous if: \(\color{blue}x\in \mathbb R\ |\ 0\le x< \infty\ and\ x\ne 3.\)

laugh  !

 Jun 10, 2022

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