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FIND THE LIMIT

As x approaches 0:

tan 5 x/sin 25 x

1 answer

use lptals rule
the derivative of tan(5x)=sec(5x)^2
the derivative of sin(25x)=cos(25x)*5
the lim of tan(5x)/(sin(25x))=the lim of
sec(5x)^2/(cos(25x)*5)
direct substution will work for this limit so I will evaluate at 0
the answer is 1/5
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