lim arcsec (x)/√(x-1)
x->1
I know from using L'Hospital's Rule that this is √2, but how do I do this w/o that rule or using derivatives?

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\[\lim_{x \rightarrow 1} (\cos^{-1} (1/x)) / \sqrt{x - 1})\]

There is a way to do this using many substitutions but it often gets complicated.

\[\mu = \sqrt{x - 1}, \mu ^{2} = x - 1, x = \mu ^{2} + 1\]

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