Posted by **APpreciative student** on Tuesday, September 14, 2010 at 10:25pm.

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**, Tuesday, September 14, 2010 at 10:27pm
see below

- calc bc (condensed -
**Reiny**, Tuesday, September 14, 2010 at 10:40pm
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**, Tuesday, September 14, 2010 at 10:47pm
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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