fundemental limit of sinx/x (1 Viewer)

[vmoore]

i know the limit of x->0 sinx/x is equal to one
but what about x/sinx
it is still 1 right - the recripical of 1 is 1.

but what about 3x/sinx
is it 3 or 1/3 ?
do you take recripical : sinx/3x then take the 1/3 out to get 1/3
or
do you take the 3 out to get x/sinx and then equal to 3?

 

[duy.le]

i know the limit of x->0 sinx/x is equal to one
but what about x/sinx
it is still 1 right - the recripical of 1 is 1.

but what about 3x/sinx
is it 3 or 1/3 ?
do you take recripical : sinx/3x then take the 1/3 out to get 1/3
or
do you take the 3 out to get x/sinx and then equal to 3?

if u take a 3 out first, yes it makes 3 but then u have to take the reciprocal again which then indeed makes 1/3, remember that u can only apply the limit thing when its in its original form or else ull get the wrong answer.

 

[munchiecrunchie]

i think you take out the 3, and depending on whether its 3x/sinx, or sinx/3x, then the answer is either 3 or 1/3.

 

[prod1gy]

hey man the answer is 3 as you take it out then balance it out, times it by 1 and done.

 

[vmoore]

im getting mixed answers...

 

[vds700]

I believe the answer is 3. You can confirm this by subbing in very small values of x into the limit, and you'll see it gets closer and closer to 3

e.g, let x = 1 x 10^-3

3(1 x 10^-3)/sin(1 x 10^-3) = 3.0000005

let x = 1 x 10^-4

3(1 x 10^-4)/sin(1 x 10^-4) = 3.000000005 etc

 

[vmoore]

yeah that makes sense, thanks vds700

although - i do have to say you are such a dork for expressing your subjects in complex numbers form
' Expressing my subjects in complex number form:
(Physics + Chem + Maths ext1 + Maths ext2 ) + i(English + SOR)'

haha but it is funny!

thanks!

 

[vds700]

yeah that makes sense, thanks vds700

although - i do have to say you are such a dork for expressing your subjects in complex numbers form
' Expressing my subjects in complex number form:
(Physics + Chem + Maths ext1 + Maths ext2 ) + i(English + SOR)'

haha but it is funny!

thanks!

I was merely making the point that english and religion are not real subjects

 

[tommykins]

Oh Lol.i Geti It.

 

[Captin gay]

Use L'Hopitals Rule

Differentiate the the numerator and denominator, then sub in the x = 0 or whateva.

 

[tommykins]

Use L'Hopitals Rule

Differentiate the the numerator and denominator, then sub in the x = 0 or whateva.

Don't know if that's allowed in the hsc lol.

 

[Captin gay]

dey betta

 

[vmoore]

Use L'Hopitals Rule

Differentiate the the numerator and denominator, then sub in the x = 0 or whateva.

i have no idea what that is... but it works!
why int it allowed... what is it ?

 

[Captin gay]

Poor fool, you'll learn it in your first university Calculus course. It works because if you zoom in close enough, the curves going thru a point look linear. Hence, the functions can be approximated by their tangents at that point (which is y u differentiate) OWWW KKKKKKKKKKKAY If i remember correctly, I think it only works for indeterminate forms