Welcome to our community

Be a part of something great, join today!

Trig limit

Petrus

Well-known member
Feb 21, 2013
739
Hello,
I got problem with understanding one exemple
$\lim_{x \to 0} \frac{x\cos(x)}{\sin(x)}$ = $\lim_{x \to 0}\frac{\cos(x)}{\sin(x)}$
if i do it backway i can see that correct with it $\frac{a/b}{c/d}$is equal to $\frac{ad}{bc}$ then i start to do the way what i type and dont get correct. Can anyone possible try explain for me thanks.


(Sorry about bad title I dont know what I should name it)
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: equal,limit,derivate

Hello Petrus,

You post is simply unreadable to me. Can you edit it, using the backslash "\" before the frac commands (and trig functions) to make it understandable?
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780
Re: equal,limit,derivate

Hello,
I got problem with understanding one exemple
lim x->0 $/frac{xcos(x)}{sin(x)} = lim x->0 $/frac{cos(x)}{sinx/x)}
if i do it backway i can see that correct with $/frace{a/b}{b/c}$=${ad}{bc}$ then i start to do the way what i type and dont get correct. Can anyone possible try explain for me thanks.


(Sorry about bad title I dont know what I should name it)
Hi Petrus!

Well... it is painfully obvious that the latex expressions are not working for you. ;-)
So I'll try to do without.

When you say (a/b) / (b/c) = (ad) / (bc) that is not correct.
It should be: (a/b) / (b/c) = (a/b) * (c/b) = (ac) / (b^2).

Note that dividing by a fraction is the same as multiplying by its inverse.
And also that multiplying 2 fractions means to multiply the numerators and separately the denominators.

To get back to your original expression, you have:

cos(x) / (sin(x) / x) = cos(x) * (x / sin(x)) = (cos(x) * x) / sin(x) = (x cos(x)) / sin(x).
 

Petrus

Well-known member
Feb 21, 2013
739
Re: equal,limit,derivate

Hi Petrus!

Well... it is painfully obvious that the latex expressions are not working for you. ;-)
So I'll try to do without.

When you say (a/b) / (b/c) = (ad) / (bc) that is not correct.
It should be: (a/b) / (b/c) = (a/b) * (c/b) = (ac) / (b^2).

Note that dividing by a fraction is the same as multiplying by its inverse.
And also that multiplying 2 fractions means to multiply the numerators and separately the denominators.

To get back to your original expression, you have:

cos(x) / (sin(x) / x) = cos(x) * (x / sin(x)) = (cos(x) * x) / sin(x) = (x cos(x)) / sin(x).
Now it make Clear! Thanks!
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780
Re: equal,limit,derivate

Now it make Clear! Thanks!
Good! ;)

For later reference: you can use \lim_{x \to 0} to format your limit nicely:
$$\lim_{x \to 0}$$