Limit Question: lim[x -> 0] [(e^x + e^{-x} - 2) / (1 - cos 2x)]

[Zoheb07]

\(\displaystyle \mbox{Determine the value of the following:}\)

. . . . .\(\displaystyle \displaystyle \lim_{x \rightarrow 0}\, \left(\dfrac{e^x\, +\, e^{-x}\, -\, 2}{1\, -\, \cos 2x}\right)\)

Can someone help me in finding the answer?

 

[Deleted member 4993]

\(\displaystyle \mbox{Determine the value of the following:}\)

. . . . .\(\displaystyle \displaystyle \lim_{x \rightarrow 0}\, \left(\dfrac{e^x\, +\, e^{-x}\, -\, 2}{1\, -\, \cos 2x}\right)\)

Can someone help me in finding the answer?

Have you tried to apply L'Hospital's rule? You may have to apply it several times!

 

[Bob Brown MSEE]

answer

1/2

Try Taylor series for e^x and cos(x)

 

[Zoheb07]

Have you tried to apply L'Hospital's rule? You may have to apply it several times!

Thanks, I had to use L'Hospital's rule twice. The teacher did explain to use L'Hospital's rule but did not mention anything about using it several time.