Tan Right
October 30th, 2009
What is the limit of (tan (2x) + cot (2x))^2011 as x approaches pi/2 from the right?
You are NOT allowed to use L’Hopital’s Rule.
I was thinking of letting y = tan (2x), so this is the limit of (y + 1/y)^2011 as y approaches 0. The limit turns out to be infinity, so there is no finite limit. Is that right?
Your solution looks mostly fine.
To elaborate a little bit:
As x –> pi/2 +, y = tan(2x) –> 0+.
So, lim(y–>0+) (y + 1/y)^2011 = +∞.
I hope this helps!
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