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Question
If the function \[f\left( x \right) = \frac{\sin 10x}{x}, x \neq 0\] is continuous at x = 0, find f (0).
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Solution
Given:
\[\Rightarrow \lim_{x \to 0} \frac{10 \sin 10x}{10x} = f\left( 0 \right)\]
\[ \Rightarrow 10 \lim_{x \to 0} \frac{\sin 10x}{10x} = f\left( 0 \right)\]
\[ \Rightarrow f\left( 0 \right) = 10\]
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