Evaluate the following limits. lim_{thetarightarrow0}frac{cos^2theta-1}{theta}

Evaluate the following limits. lim_{thetarightarrow0}frac{cos^2theta-1}{theta}

Question
Limits and continuity
asked 2020-11-14
Evaluate the following limits.
\(\lim_{\theta\rightarrow0}\frac{\cos^2\theta-1}{\theta}\)

Answers (1)

2020-11-15
Given that \(\lim_{\theta\rightarrow0}\frac{\cos^2\theta-1}{\theta}\)
Compute the limit as follows.
\(\lim_{\theta\rightarrow0}\frac{\cos^2\theta-1}{\theta}=\lim_{\theta\rightarrow0}\frac{-(1-\cos^2\theta)}{\theta}\)
\(=\lim_{\theta\rightarrow0}\frac{-\sin^2\theta}{\theta}\)
\(=\lim_{\theta\rightarrow0}\frac{\sin\theta}{\theta}\times\lim_{\theta\rightarrow0}(-\sin\theta)\)
\(=1\times(0)\)
\(=0\)
Thus, \(\lim_{\theta\rightarrow0}\frac{\cos^2\theta-1}{\theta}=0\)
0

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