First slide

Continuity

Question

$The function f (x) = \frac{x \tan 2 x}{\sin 3 x \cdot \sin 5 x} for x \neq 0 is continuous at x = 0 then f (0)$

Moderate

Solution

$f (0) = K = \underset{x \to 0}{L t} \frac{x \tan 2 x}{\sin 3 x . \sin 5 x}$
$\begin{array}{l} = \underset{x \to 0}{L t} \frac{\frac{x \tan 2 x}{x^{2}}}{\frac{\sin 3 x}{x} . \frac{\sin 5 x}{x}} \\ = \frac{2}{15} \end{array}$

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