Simple limit question (1 Viewer)

[jiminymacca]

I can't seem to find it in my Maths in Focus text books but why when solving a limit such as
.
Lim sin3x
x>0 x
.
Why do you have to divide by 1/3 on the inside and multiply by 3 on the outside...I don't remember covering that. :S

Thanks guys

 

[Timothy.Siu]

seems right
jst remember sin x/x -->1 as x-->infinity

so sin 9999999x/9999999x =1 too

 

[jiminymacca]

Its more WHY you have to do that, now how or what you have to do..

 

[scardizzle]

3x does not = x so lets just say 3x = z

sinz/x doesnt not = 1 to get it into the form sinx/x (a result we know) we multiply 1/3 since x/3 = z but this would change the value of the original equation so we also multiply by 3 so that we get (sinz/z) x 3 or (sin3x/3x) x 3

 

[addikaye03]

I can't seem to find it in my Maths in Focus text books but why when solving a limit such as
.
Lim sin3x
x>0 x
.
Why do you have to divide by 1/3 on the inside and multiply by 3 on the outside...I don't remember covering that. :S

Thanks guys

lim(x-->0) sin3x/x x 3/3 (which is the same as multiplying by 1)

therefore lim(x-->0) sin3x/3x x 3/1

Therfore 1 x 3 =3

-Solution isn't 1/3