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| Math Central | Quandaries & Queries |
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Berta, a student: Evaluate limit xcsc2x/cos 5x as x goes to 0 |
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.
Penny
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