Find the limit. lim_(xrightarrow 0)((x csc 2x))/(cos 5x)

empalhaviyt 2022-08-08 Answered
Find the limt. lim x 0  ( x csc 2 x ) cos 5 x
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Answers (2)

Jaelyn Rosario
Answered 2022-08-09 Author has 16 answers
lim x 0 ( x csc 2 x ) cos 5 x = lim x 0 x sin 2 x ( cos 5 x )
= lim x 0 1 2 cos 2 x ( cos 5 x ) 5 sin 2 x sin 5 x = 1 2 cos ( 2 0 ) cos ( 5 0 ) 5 sin ( 2 0 ) sin ( 5 0 )
= 1 2 1 1 5 0 0 = 1 2
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Lacey Rojas
Answered 2022-08-10 Author has 2 answers
l i m x 0 ( x csc ( 2 x ) ) / ( cos ( 5 x ) = lim x 0 ( 1 / 2 ) ( 2 x / sin ( 2 x ) ) / cos ( 5 x )
Now lim x 0 sin ( 2 x ) / 2 x = 1   a n d   lim x 0 cos ( 5 x ) = 1
so lim x 0 ( x csc ( 2 x ) ) / ( cos ( 5 x ) = 1 / 2
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