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Section 3-5 : Derivatives of Trig Functions

1. Evaluate \(\displaystyle \mathop {\lim }\limits_{z \to \,0} \frac{{\sin \left( {10z} \right)}}{z}\) .

Show Solution

All we need to do is set this up to allow us to use the fact from the notes in this section.

\[\mathop {\lim }\limits_{z \to \,0} \frac{{\sin \left( {10z} \right)}}{z} = \mathop {\lim }\limits_{z \to \,0} \frac{{10\sin \left( {10z} \right)}}{{10z}} = 10\mathop {\lim }\limits_{z \to \,0} \frac{{\sin \left( {10z} \right)}}{{10z}} = 10\left( 1 \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{10}}\]