Question

Lim x=1 √((x*x)-1) +√(x-1) / √((x*x)-1)​

Answer 1

Answer:

limx→01+x−−−−−√−1−x−−−−−√x=limx→01+x−−−−−√−1−x−−−−−√x⋅1+x−−−−−√+1−x−−−−−√1+x−−−−−√+1+x−−−−−√=limx→0(1+x)−(1−x)x(1+x−−−−−√+1−x−−−−−√)=limx→021+x−−−−−√+1−x−−−−−√=21+0−−−−√+1−0−−−−√=1

Or by using binomial series for small numbers, we have 1+x−−−−−√≈1+0.5x and similar tricks for the other square root term.

Then it is easy to see that both numerator and denominator are x, so the answer

is

Step-by-step explanation:

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