Sarah J.

asked • 09/22/14

find the limit of (1-cos2x-cos4x)/x as x->0 and show all work!

fin the limit of (1-cos2x-cos4x)/x as x->0 and show all work!

3 Answers By Expert Tutors

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SURENDRA K. answered • 09/22/14

An experienced,patient & hardworking tutor

Yohan C.

You are right on that.  I had to leave the page (screen) for while.  I couldn't finish it.
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09/23/14

Nadia N. answered • 09/22/14

Effective Mathematics Tutor

Yohan C. answered • 09/22/14

Math Tutor (up to Calculus) (not Statistics and Finite)

Yohan C.

I didn't calculate second part (cos 4x / x).  Here is how I did it and it came out to be  ∞ or doesn't exist.
 
lim     cos 4x   =    4 cos 4x    =    4 lim  cos 4x   =   4 lim cos u    =   4 lim [ ln cos u]
x->0     x                   4x                          4x                     u                         [ u ]
 
ln cos u becomes ln 1 which is 0 but [ -ln 1/u] or ln u or ln 0 which it gives undefined value (∞).  If this limit is approaching 0+ from the right, -∞ might have been the answer.  But since it approaches 0, this limit doesn't exists.
 
Sorry for mishap.
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09/23/14

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