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0 votes
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in Limits by (15 points)
Somebody please elaborate on how to use L'hopital's rule in this item?

lim (x-pi/2) tanx as it approaches x->pi/2

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1 Answer

+1 vote
by (518 points)

Ans: -1


Question says: \( \lim\limits_{x \to \pi/2} (x-\pi/2)Tanx\)

Now, lets assume Cotx = t

So, question changes to : \( \lim\limits_{t\to 0} (arc cot(t)-\pi/2)/t\) which if a 0/0 indeterminate fom and thus you can apply L’hopital rule as:

\(\lim\limits_{t\to 0} (arc cot(t)-\pi/2)/t = \lim\limits_{t\to 0} -1/(1+t^2) = -1\)

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