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## anonymous 5 years ago limit as x approaches 0 of (sin 5x)/7x?

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1. anonymous

I've considered multiply the numerator by 5x/5x so that sin x will become 1 as x approaches zero...but doesn't the problem then become 5x/7x and they both go to zero?

2. myininaya

$\lim_{x \rightarrow 0}\frac{\sin(5x)}{5x} =1$ right? so how do we get this in our problem? $\frac{5}{7}\lim_{x \rightarrow 0}\frac{\sin(5x)}{5x}$

3. cathyangs

wouldn't there be no limit? *confuzzled* O.o

4. myininaya

$\frac{5}{7}(1)=\frac{5}{7}$

5. anonymous

Sorry, is there an intermediate step missing?

6. TuringTest

You can verify that myininaya is right very quickly if you know L'hospital's rule.

7. myininaya

all i did was multiply 5/5 @ josh

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