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Help finding a limit

  • #1

Homework Statement


[tex]\mathop {\lim }\limits_{x \to 0} (1 - \cos x)[/tex]

2. The attempt at a solution

well as x goes to 0, cos x goes to 1... ln(1-1) is undefined
now if I forget about plugging in x=0 and think a little bit, the ln argument gets very very small, and the logarithm of a decimal number is a negative number... so I would say the limit is minus infinity.

however, is it possible to get that result analytically.... by transforming/simplyfing/etc. the function?

sorry, I have just finished precalculus and I am beginning calculus, so my calculus skills are crap =\

thank you
 
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Answers and Replies

  • #2
1,752
1
hmm ... problem is: [tex]\lim_{x\rightarrow0}(1-\cos x)[/tex]?

Can't you just plug it in?

Or is it:

[tex]\lim_{x\rightarrow0}\ln{(1-\cos x)}[/tex]

Ok so have the graph infront of you. You know as you "approach" coming from the right, it's negative infinity ...

[tex]\lim_{x\rightarrow0^{+}}\ln{(1-\cos x)}=-\infty[/tex]

What about from the left? Because in order for the Limit to exist, the L & R Limits must agree. But for the natural logarithm, how is it uniquely defined?
 
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  • #3
1
0
Once you have learned L^Hopitals rule, you will be able to apply it to this equation and get the same answer analytically.
 

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