Limit Problem- Please help- It's easy but my TI broke:(

mathqueen88

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Sep 10, 2010
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f(x) = (3)(cos2x-1) / 4x^2


x->0


Now basically the 2 between cos - x is a square , and so is the 2 in the denominator .


The question is, what is the Right hand Limit and Left hand limit ( I got .347 and 0 ) respectively,

And what is the normal limit ? ( I got DNE)
 
f(x) = 3cos(2x1)4x2\displaystyle f(x) \ = \ \frac{3cos(2x-1)}{4x^2}

limx0f(x) = 3cos(1)0 = .\displaystyle \lim_{x\to0}f(x) \ = \ \frac{3cos(-1)}{0} \ = \ \infty.
 
the Cos is squared, that is not a 2x but instead a cos^2(x) so thus cos(x)^2

and I asked for left and right hand limit too :)
 
Hey mathqueen88, Im not a Swami, perhaps others on this board are.\displaystyle Hey \ mathqueen88, \ I'm \ not \ a \ Swami, \ perhaps \ others \ on \ this \ board \ are.

cos(2x)  cos2(x) and cos2(x) = [cos(x)]2  cos(x)2.\displaystyle cos(2x) \ \ne \ cos^2(x) \ and \ cos^2(x) \ = \ [cos(x)]^2 \ \ne \ cos(x)^2.

Learn your grouping symbols as, at present, theyre atrocious.\displaystyle Learn \ your \ grouping \ symbols \ as, \ at \ present, \ they're \ atrocious.
 
mathqueen88 said:

f(x) = (3)(cos2x-1) / 4x^2


x->0


Now basically the 2 between cos - x is a square , and so is the 2 in the denominator .


The question is, what is the Right hand Limit and Left hand limit ( I got .347 and 0 ) respectively,

And what is the normal limit ? ( I got DNE)

After all the explanation:

limx03[cos2(x)1]4x2\displaystyle \lim_{x\to 0}\frac{3[cos^2(x) - 1]}{4x^2}

Does your problem look like the above?
 
An another thing, if your problem is what Subhotosh Khan has quoted above,\displaystyle An \ another \ thing, \ if \ your \ problem \ is \ what \ Subhotosh \ Khan \ has \ quoted \ above,

then the limit as x approaches 0, 0, and 0+ is 3/4, not the crap that you have\displaystyle then \ the \ limit \ as \ x \ approaches \ 0, \ 0^-, \ and \ 0^+ \ is \ -3/4, \ not \ the \ crap \ that \ you \ have

expounded.\displaystyle expounded.
 
limx03(cos2(x)1)4x2\displaystyle \lim_{x\to 0}\frac{3(cos^{2}(x)-1)}{4x^{2}}

Note that cos2(x)1=sin2(x)\displaystyle cos^{2}(x)-1=-sin^{2}(x)

So, we get:

34limx0sin2(x)x2\displaystyle \frac{-3}{4}\lim_{x\to 0}\frac{sin^{2}(x)}{x^{2}}

34limx0(sin(x)x)2\displaystyle \frac{-3}{4}\lim_{x\to 0}\left(\frac{sin(x)}{x}\right)^{2}

Remember what limx0sin(x)x\displaystyle \lim_{x\to 0}\frac{sin(x)}{x} equals?.

See the limit now?. Since the limit exists, the right limit and left limit are the same.

By the way, use the ^ key for powers. Writing cos2x when you mean cos2(x)\displaystyle cos^{2}(x) is going to confuse anyone.

Afterall, that is what the SHIFT 6 key is for.
 
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