Limits involving cosine

  • Thread starter mtayab1994
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  • #1
mtayab1994
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Homework Statement


find the limit of :

[tex]\lim_{x\rightarrow0}\frac{\sqrt{5-cos(x)}-2}{x^{2}}[/tex]


Homework Equations





The Attempt at a Solution



I multiplied the numerator and the denominator by the conjugate of the numerator and i got :

[tex]\frac{1-cos(x)}{x^{2}(\sqrt{5-cos(x)}+2)}[/tex]

then: i divided top and bottom by x^2 and i got (1/2)/4 which is 1/8.

Is what I have done correct?
 
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Answers and Replies

  • #2
tiny-tim
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hi mtayab1994! :smile:
I multiplied the numerator and the denominator by the conjugate of the numerator and i got :

[tex]\frac{1-cos(x)}{x^{2}(\sqrt{5-cos(x)}+2)}[/tex]

then: i divided top and bottom by x and i got (1/2)/4 which is 1/8.

Is what I have done correct?

oooh, I've never seen that trick before! :tongue2:

yes, that's fine

(the usual way of dealing with cosx is to replace it by 1 - x2/2 … same result)
 
  • #3
mtayab1994
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Yea thanks. And by the way I didn't know that you replace cos x with 1-x^2/2. Well maybe it's because we haven't done it yet.
 
  • #4
tiny-tim
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ah!

yes, cos x = 1 - x2/2 + x4/4! - x6/6! + …

you'll learn about that later :smile:
 
  • #5
mtayab1994
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ah!

yes, cos x = 1 - x2/2 + x4/4! - x6/6! + …

you'll learn about that later :smile:

Alrighty thank you very much. I live in morocco and I'm in kind of like in a "Math-Science" major in high school so we're really big on math and physics over here.
 

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