Math CentralQuandaries & Queries


Berta, a student:

Evaluate limit xcsc2x/cos 5x as x goes to 0
ans is 2 but I get 1/2
x/sin2xcos5x = 2x/2sin2xcos5x= 1/2cos5x

Hi Berta,

I also get 1/2 but you need to be more careful when you write a solution. I agree that

xcsc2x/cos 5x = x/sin2xcos5x = 2x/(2sin2xcos5x)

but in the next step you need to use the limit.

lim(2x/2sin2xcos5x) = 1/2 lim(2x/sin2x) lim(1/cos5x) = 1/2 x 1 x 1 = 1/2.


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