Question

limit as x approaches 0 of (sin 5x)/7x?

Answer 1

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?

Answer 2

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

Answer 3

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

Answer 4

\[\frac{5}{7}(1)=\frac{5}{7}\]

Answer 5

Sorry, is there an intermediate step missing?

Answer 6

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

Answer 7

all i did was multiply 5/5 @ josh