Can anyone help me with this?

[meager stratus]

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[obsidian stirrup]

I don’t think it’s defined because depending if x tends from the left or right side the denominator is going to be either always 0 or always 1

$\tan(x)=x+\frac{x^{3}}{3} +o(x^{4})$

[frank nymph]

Rotor

[obsidian stirrup]

For x approaching 0

now if x<0 you can see that around 0 tan(x)<x but if x>0 tan(x)>x

so if x tends from the left side you will get 0 for the denom and 1 if it’s from the right side

likewise depending on from which side x tends you have asymptotically sin(x)<x for x>0 and sin(x)>x for x<0

So one of both tends to 0 or 1

in the sum I mean

@dense obsidian

[dense obsidian]

Mmmm, But here they didn't say anything like x is approaching from left or right

[obsidian stirrup]

No I think I got confused i any case tan(x)/x>1

because either tan(x)>x for x>0 or tan(x)<x for x<0 so tan(x)/x>1 in any case

So the denominator tends to 1

[dense obsidian]

Okk Hmhm

[dense obsidian]

Yes 👍

So denominator is 1

@obsidian stirrup

Can't we say

that

when x is tending to 0

Sinx is approximately equal to x

But these espressions "Sinx/x" and x/Sinx"

are not defined at x = 0

[obsidian stirrup]

yes we can but here its the greatest integer function so you need to see if sin(x)/x<1 or sin(x)/x>1 for x approching 0 so depending on that fact the function is going to be 0 or 1 when x >0 sin(x)<x and for x<0 sin(x)>x but in any case you have sin(x)/x<1 and x/sin(x)>1

because around 0 sin(x)=x-x^3/6 +o(x^4)

so you can conclude

[dense obsidian]

Mmmm, so it's -1

[obsidian stirrup]

well considering around 0 sin(x)/x <1 then floor(sin(x)/x)=0 for x approaching 0

and floor(x/sin(x))=1 for x approaching 0

[dense obsidian]

Yes

[obsidian stirrup]

as ive said

and weve established that floor(tan(x)/x) is 1 as x approaches 0

[dense obsidian]

Ok @obsidian stirrup

Thanks for your help 🙂

I understood

Umm, How to give a rep point for you?

lol

[obsidian stirrup]

thanks

reply by thanking me if you want to give rep points

[arctic hinge]

@obsidian stirrup has given 1 rep to @dense obsidian

[ocean summit]

ill do it for u

thanks @obsidian stirrup

[arctic hinge]

@ocean summit has given 1 rep to @obsidian stirrup

[dense obsidian]

thanks @obsidian stirrup

[arctic hinge]

@dense obsidian has given 1 rep to @obsidian stirrup

[dense obsidian]

+close