Posted by APpreciative student on .
is the limit as x approaches 0 of sin3x over 3x equal to zero?
sorry
basically this is my problem:
lim [sin 3x / 4x)
x> 0
~~~~I multiplied& eventually got to
.75* lim (sin 3x / 3x)
x> 0
~so i figured since (lim (sinx/x)
x> 0
was equal to zero, then
lim (sin3x/ 3x) also equaled 0
x> 0
is that right? thank you !!!
(all of the x> 0 should be under the "lim"  just in case the text shifts...)

calc bc (condensed 
TutorCat,
see below

calc bc (condensed 
Reiny,
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 
calc bc (condensed 
Reiny,
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