Posted by APpreciative student on Tuesday, September 14, 2010 at 10:25pm.
see below
your preliminary steps are correct
lim sin3x/(4x) as x--> 0
= lim (3/4)(sin3x/(3x))
= 3/4(1)
= 3/4
lim sinx/x = 1 not zero
as x-->0
continued..
Here is a simple way to check your limit answers if you have a calculator
pick a value very "close" to your approach value, in this case I would pick x = .001
evaluate using that value, (you are not yet dividing by zero, but close)
for your question I got .749998875, close to 3/4 I would say.
PS. Make sure your calculator is set to Radians
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