Respuesta :

nobillionaireNobley
To evaluate
[tex] \lim_{\theta \to 0} \frac{\sin\theta}{\theta} [/tex]

First, we input 0, for theta in the function to obtain:
[tex] \frac{\sin0}{0} = \frac{0}{0} [/tex]

This is an indeterminate form.

So, we apply L'Hopital's rule by differentiating the numerator and the denominator as follows:

[tex]\lim_{\theta \to 0} \frac{\sin\theta}{\theta}=\lim_{\theta \to 0} \frac{ \frac{d}{d\theta} (\sin\theta)}{\frac{d}{d\theta}\theta} \\ \\ =\lim_{\theta \to 0} \frac{\cos\theta}{1}=\cos0=1[/tex]

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