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Problem 39 Medium Difficulty

Find the limit.
$ \displaystyle \lim_{x\to 0} \frac {\sin - 5x}{3x} $

Answer

$\frac{5}{3}$

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Video Transcript

it's clear. So when you married here. So we're gonna find the limit. As X goes to therapy, we're sign five X over three eggs. So our goal here is charging me five x in the denominator. So we're going to multiply 5/3 times 3/5. This becomes 5/3 limit. Thanks. Approaches. Ciro three sign five X over five times three x and then we could simplify this into five birds limit. So that's approaches. Ciro. Their sign five Lex over five x and we're going to use you. Gonna substitute five x by you, which is equal to 5/3 limit as you approach is Ciro for a sign you over you. So we see that the limit X approaches syrup of sine X over X is equal to one, so it's 5/3 times one is equal to 5/3.