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

Evaluate the following limits.
$\underset{\theta \to 0}{lim}\frac{{\mathrm{cos}}^{2}\theta -1}{\theta }$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Raheem Donnelly
Given that $\underset{\theta \to 0}{lim}\frac{{\mathrm{cos}}^{2}\theta -1}{\theta }$
Compute the limit as follows.
$\underset{\theta \to 0}{lim}\frac{{\mathrm{cos}}^{2}\theta -1}{\theta }=\underset{\theta \to 0}{lim}\frac{-\left(1-{\mathrm{cos}}^{2}\theta \right)}{\theta }$
$=\underset{\theta \to 0}{lim}\frac{-{\mathrm{sin}}^{2}\theta }{\theta }$
$=\underset{\theta \to 0}{lim}\frac{\mathrm{sin}\theta }{\theta }×\underset{\theta \to 0}{lim}\left(-\mathrm{sin}\theta \right)$
$=1×\left(0\right)$
$=0$
Thus, $\underset{\theta \to 0}{lim}\frac{{\mathrm{cos}}^{2}\theta -1}{\theta }=0$
Jeffrey Jordon