What is $ \lim_{x \to 1} - 1}{x^{(n+1)} - 1} $ equal to, where $ n 1 $ is a natural number ?

Question

What is $ \lim_{x \to 1} - 1}{x^{(n+1)} - 1} $ equal to, where $ n > 1 $ is a natural number ?

SquadPrep · Accepted Answer

n - 1. Applying L'Hopital's rule, differentiate the numerator and denominator to get $ }{(n+1)x^n} $. Substituting x=1 yields $ {n+1} = n-1 $.

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What is \( \lim_{x \to 1} \frac{x^{(n^2 - 1)} - 1}{x^{(n+1)} - 1} \) equal to, where \( n > 1 \) is a natural number ?