I have this question in my book and the answer amounts to

I assume it would need to be

aidinacol7
2022-04-03
Answered

Evaluating $\underset{x\to 0}{lim}\frac{1-\mathrm{cos}x}{{\left(2x\right)}^{2}}$

I have this question in my book and the answer amounts to$\frac{1}{4}$ . I don't see how, and I think it's an error. Can you confirm it is an error?

$\underset{x\to 0}{lim}\frac{1-\mathrm{cos}x}{{\left(2x\right)}^{2}}$

I assume it would need to be${\mathrm{cos}}^{2}x$ instead.

I have this question in my book and the answer amounts to

I assume it would need to be

You can still ask an expert for help

membatas0v2v

Answered 2022-04-04
Author has **19** answers

It's indeed not correct. Simply use l'Hopital rule allow you to conclude that

$\underset{x\to 0}{lim}\frac{1-\mathrm{cos}\left(x\right)}{{\left(2x\right)}^{2}}=\underset{x\to 0}{lim}\frac{1-\mathrm{cos}\left(x\right)}{4{x}^{2}}=\underset{x\to 0}{lim}\frac{\mathrm{sin}\left(x\right)}{8x}=\frac{1}{8}$

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Consider the three following matrices:

$A=\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& 0\\ 0& 0& 1\end{array}\right],B=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 0\\ 0& 0& -1\end{array}\right]\text{and}C=\left[\begin{array}{ccc}0& -i& 0\\ i& 0& -i\\ 0& i& 0\end{array}\right]$

Calculate the Tr(ABC)

(a)1

(b)2

(c)2i

(d)0

Calculate the Tr(ABC)

(a)1

(b)2

(c)2i

(d)0